Finite Group Databasebeta

← Group #72253360

Character table — Group #72253360

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222222222222444444444444444488888888881616161616161616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order12222222223444444446661212121222226666661212121212124466661212121244448888888812121212121212122424242424242424242424242424242422222222244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111
χ1011111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-11111-1-1
χ1111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ1211111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1311111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1411111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ1511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ1611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-200002i−2i2i−2i0000000000002i2i−2i−2i00002i2i−2i−2i000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-20000−2i2i−2i2i000000000000−2i−2i2i2i0000−2i−2i2i2i000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2222200002i−2i−2i2i000000000000−2i−2i2i2i00002i2i−2i−2i000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-222220000−2i2i2i−2i0000000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000
χ212222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ222222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ232222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-11111-1-1-1-1111100000000000000000000
χ242222222222-122222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222111111111111-1-1-1-11111-1-1-1-100000000000000000000
χ252222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111122-2-222-2-2-2-222-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000
χ262222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111122-2-2-2-22222-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000
χ272222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111-2-22222-2-222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ282222222222-122222222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111-2-222-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ292222222222-1-2-2-2-2-2-2-2-2-1-1-111112222-1-1-1-1-1-1111111-2-2-1-1-1-1111100002i−2i2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii33−3−3−i−iii33−3−300000000000000000000
χ302222222222-1-2-2-2-2-2-2-2-2-1-1-111112222-1-1-1-1-1-1111111-2-2-1-1-1-1111100002i−2i2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−3−333−i−iii−3−33300000000000000000000
χ312222222222-1-2-2-2-2-2-2-2-2-1-1-111112222-1-1-1-1-1-1111111-2-2-1-1-1-111110000−2i2i−2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−i−3−333ii−i−i−3−33300000000000000000000
χ322222222222-1-2-2-2-2-2-2-2-2-1-1-111112222-1-1-1-1-1-1111111-2-2-1-1-1-111110000−2i2i−2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−i33−3−3ii−i−i33−3−300000000000000000000
χ332222222222-1-2-2-2-2-2-2-2-2-1-1-11111-2-2-2-2-1-1-1-1-1-1111111221111-1-1-1-100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−3−333−i−iii33−3−300000000000000000000
χ342222222222-1-2-2-2-2-2-2-2-2-1-1-11111-2-2-2-2-1-1-1-1-1-1111111221111-1-1-1-100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i33−3−3−i−iii−3−33300000000000000000000
χ352222222222-1-2-2-2-2-2-2-2-2-1-1-11111-2-2-2-2-1-1-1-1-1-1111111221111-1-1-1-10000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3−i−iii33−3−3ii−i−i−3−33300000000000000000000
χ362222222222-1-2-2-2-2-2-2-2-2-1-1-11111-2-2-2-2-1-1-1-1-1-1111111221111-1-1-1-10000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3−i−iii−3−333ii−i−i33−3−300000000000000000000
χ3722222-2-2-22-22-2-22-222-22222-2-2-2-200002-2-2-2-2222-2-22200000000002-200000000002-22-20000000000000000000022-2-2000000002-2000000
χ3822222-2-2-22-22-2-22-222-22222-2-2-2-200002-2-2-2-2222-2-22200000000002-200000000002-22-200000000000000000000-2-22200000000-22000000
χ3922222-2-2-22-22-2-22-222-22222-2-2-2-200002-2-2-2-2222-2-2220000000000-220000000000-22-220000000000000000000022-2-200000000-22000000
χ4022222-2-2-22-22-2-22-222-22222-2-2-2-200002-2-2-2-2222-2-2220000000000-220000000000-22-2200000000000000000000-2-222000000002-2000000
χ412222-22-2-2-2222-2-222-2-2222222220000-222-2-2-22-2-2-22-20000000000000000002-2000000000000002-22-200000000000022-2-22-20000000000
χ422222-22-2-2-2222-2-222-2-2222222220000-222-2-2-22-2-2-22-20000000000000000002-2000000000000002-22-2000000000000-2-222-220000000000
χ432222-22-2-2-2222-2-222-2-2222222220000-222-2-2-22-2-2-22-2000000000000000000-2200000000000000-22-2200000000000022-2-2-220000000000
χ442222-22-2-2-2222-2-222-2-2222222220000-222-2-2-22-2-2-22-2000000000000000000-2200000000000000-22-22000000000000-2-2222-20000000000
χ452-2-22222-2-2-22222-2-2-2-22-2-2222-2-2000022-22-2-2-2-22-2220000000000002i−2i0000000000002i−2i2i−2i00000000000000002-22-200000000002i−2i0000
χ462-2-22222-2-2-22222-2-2-2-22-2-2222-2-2000022-22-2-2-2-22-2220000000000002i−2i0000000000002i−2i2i−2i0000000000000000-22-220000000000−2i2i0000
χ472-2-22222-2-2-22222-2-2-2-22-2-2222-2-2000022-22-2-2-2-22-222000000000000−2i2i000000000000−2i2i−2i2i00000000000000002-22-20000000000−2i2i0000
χ482-2-22222-2-2-22222-2-2-2-22-2-2222-2-2000022-22-2-2-2-22-222000000000000−2i2i000000000000−2i2i−2i2i0000000000000000-22-2200000000002i−2i0000
χ492-2-222-2-22-22222-2-222-2-2-2-2222-2-222-2-22-22-22-2222-2-2-22-222-2-222-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ502-2-222-2-22-22222-2-222-2-2-2-2222-2-222-2-22-22-22-2222-2-2-22-222-2-222-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ512-2-222-2-22-22222-2-222-2-2-2-2222-2-2-2-2222-22-22-2222-2-2-2-22-2-222-2-22200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ522-2-222-2-22-22222-2-222-2-2-2-2222-2-2-2-2222-22-22-2222-2-2-2-22-2-222-2-2220000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ532-2-222-2-22-222-2-222-2-222-2-22-2-22222-2-22-22-22-2-2-2-2222-2222-2-2-2-2220000000000000000000000000000000000002-2-222-22-2000000000000
χ542-2-222-2-22-222-2-222-2-222-2-22-2-22222-2-22-22-22-2-2-2-2222-2222-2-2-2-222000000000000000000000000000000000000-222-2-22-22000000000000
χ552-2-222-2-22-222-2-222-2-222-2-22-2-222-2-2222-22-22-2-2-2-22222-2-2-22222-2-20000000000000000000000000000000000002-2-22-22-22000000000000
χ562-2-222-2-22-222-2-222-2-222-2-22-2-222-2-2222-22-22-2-2-2-22222-2-2-22222-2-2000000000000000000000000000000000000-222-22-22-2000000000000
χ572-2-22-2-22-2222-22-22-22-22-2-22-2-2220000-2-222-22-222-22-2000000000000000000002-2000000000000000000002-22-200002-2-22002-200000000
χ582-2-22-2-22-2222-22-22-22-22-2-22-2-2220000-2-222-22-222-22-2000000000000000000002-2000000000000000000002-22-20000-222-200-2200000000
χ592-2-22-2-22-2222-22-22-22-22-2-22-2-2220000-2-222-22-222-22-200000000000000000000-2200000000000000000000-22-2200002-2-2200-2200000000
χ602-2-22-2-22-2222-22-22-22-22-2-22-2-2220000-2-222-22-222-22-200000000000000000000-2200000000000000000000-22-220000-222-2002-200000000
χ6144444-4-4-44-4444-44-4-44-4444444400004-4-4-4-44-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ6244444-4-4-44-4-244-44-4-44-4-2-2-2-2-2-2-20000-22222-222-2-2220000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ6344444-4-4-44-4-244-44-4-44-4-2-2-2-2-2-2-20000-22222-222-2-22200000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ6444444-4-4-44-4-2-4-44-444-44-2-2-222220000-22222-2-2-222-2-200000000004-40000000000-22-220000000000000000000000000000000000000000
χ6544444-4-4-44-4-2-4-44-444-44-2-2-222220000-22222-2-2-222-2-20000000000-4400000000002-22-20000000000000000000000000000000000000000
χ664444-44-4-4-444-444-4-444-4444-4-4-4-40000-444-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000000000
χ674444-44-4-4-44-24-4-444-4-44-2-2-2-2-2-2-200002-2-2222-2222-220000000000000000004-400000000000000-22-220000000000000000000000000000
χ684444-44-4-4-44-24-4-444-4-44-2-2-2-2-2-2-200002-2-2222-2222-22000000000000000000-44000000000000002-22-20000000000000000000000000000
χ694444-44-4-4-44-2-444-4-444-4-2-2-2222200002-2-22222-2-2-22-2000000000000000000000000000000000023−23−23230000000000000000000000000000
χ704444-44-4-4-44-2-444-4-444-4-2-2-2222200002-2-22222-2-2-22-20000000000000000000000000000000000−232323−230000000000000000000000000000
χ714444-4-444-4-444-444-44-4-444444440000-4-4-444-4-44-4-4-44000000000000000000000000000000000000000000000000000000000000000000
χ724444-4-444-4-44-44-4-44-444444-4-4-4-40000-4-4-444-44-4444-4000000000000000000000000000000000000000000000000000000000000000000
χ734444-4-444-4-4-24-444-44-4-4-2-2-2-2-2-2-20000222-2-222-2222-2000000000000000000000000000000−2i32i3−2i32i300000000000000000000000000000000
χ744444-4-444-4-4-24-444-44-4-4-2-2-2-2-2-2-20000222-2-222-2222-20000000000000000000000000000002i3−2i32i3−2i300000000000000000000000000000000
χ754444-4-444-4-4-2-44-4-44-444-2-2-222220000222-2-22-22-2-2-2200000000000000000000000000000023−23−232300000000000000000000000000000000
χ764444-4-444-4-4-2-44-4-44-444-2-2-222220000222-2-22-22-2-2-22000000000000000000000000000000−232323−2300000000000000000000000000000000
χ774-4-44444-4-4-44-4-4-44444-4-4-44-4-444000044-44-4-444-44-4-4000000000000000000000000000000000000000000000000000000000000000000
χ784-4-44444-4-4-4-2444-4-4-4-4422-2-2-2220000-2-22-22222-22-2-20000000000004i−4i000000000000−2i2i−2i2i000000000000000000000000000000000000
χ794-4-44444-4-4-4-2444-4-4-4-4422-2-2-2220000-2-22-22222-22-2-2000000000000−4i4i0000000000002i−2i2i−2i000000000000000000000000000000000000
χ804-4-44444-4-4-4-2-4-4-44444-422-222-2-20000-2-22-222-2-22-2220000000000000000000000000023−23−2323000000000000000000000000000000000000
χ814-4-44444-4-4-4-2-4-4-44444-422-222-2-20000-2-22-222-2-22-22200000000000000000000000000−232323−23000000000000000000000000000000000000
χ824-4-444-4-44-44-244-4-444-4-422-2-2-22244-4-4-22-22-22-2-2-22224-4-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-44-244-4-444-4-422-2-2-222-4-444-22-22-22-2-2-2222-4422-2-222-2-200000000000000000000000000000000000000000000000000000000
χ844-4-444-4-44-44-2-4-444-4-44422-222-2-244-4-4-22-22-22222-2-2-2-44-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ854-4-444-4-44-44-2-4-444-4-44422-222-2-2-4-444-22-22-22222-2-2-24-422-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ864-4-44-44-444-444-4-4-4-4444-4-4444-4-40000-44-4-444-44-444-4000000000000000000000000000000000000000000000000000000000000000000
χ874-4-44-44-444-44-44444-4-4-4-4-44-4-4440000-44-4-4444-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ884-4-44-44-444-4-24-4-4-4-444422-2-2-22200002-222-2-22-22-2-220000000000000000000000000000000000000023−2323−23000000000000000000000000
χ894-4-44-44-444-4-24-4-4-4-444422-2-2-22200002-222-2-22-22-2-2200000000000000000000000000000000000000−2323−2323000000000000000000000000
χ904-4-44-44-444-4-2-44444-4-4-422-222-2-200002-222-2-2-22-222-200000000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ914-4-44-44-444-4-2-44444-4-4-422-222-2-200002-222-2-2-22-222-2000000000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ924-4-44-4-44-44444-44-44-44-4-4-4444-4-40000-4-444-444-4-44-44000000000000000000000000000000000000000000000000000000000000000000
χ934-4-44-4-44-444-24-44-44-44-422-2-2-222000022-2-22-2-222-22-200000000000000000000000000000000000000000023−23−232300000000000000000000
χ944-4-44-4-44-444-24-44-44-44-422-2-2-222000022-2-22-2-222-22-2000000000000000000000000000000000000000000−232323−2300000000000000000000
χ954-4-44-4-44-444-2-44-44-44-4422-222-2-2000022-2-22-22-2-22-22000000000000000000004-400000000000000000000-22-2200000000000000000000
χ964-4-44-4-44-444-2-44-44-44-4422-222-2-2000022-2-22-22-2-22-2200000000000000000000-44000000000000000000002-22-200000000000000000000
χ9788-8-80000008000000008-8-800004-44-4000000000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ9888-8-80000008000000008-8-80000-44-4400000000000000-44-44000000000000000000000000000000000000000000000000000000000000
χ9988-8-8000000-400000000-44443−4343−434-44-400000000000000-22-2223−2323−2300000000000000000000000000000000000000000000000000000000
χ10088-8-8000000-400000000-44443−4343−43-44-44000000000000002-22-2−2323−232300000000000000000000000000000000000000000000000000000000
χ10188-8-8000000-400000000-444−4343−43434-44-400000000000000-22-22−2323−232300000000000000000000000000000000000000000000000000000000
χ10288-8-8000000-400000000-444−4343−4343-44-44000000000000002-22-223−2323−2300000000000000000000000000000000000000000000000000000000
χ1038-88-8000000800000000-88-800004-4-44000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ1048-88-8000000800000000-88-80000-444-400000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ1058-88-8000000-4000000004-4443−43−43434-4-4400000000000000-222-223−23−232300000000000000000000000000000000000000000000000000000000
χ1068-88-8000000-4000000004-4443−43−4343-444-4000000000000002-2-22−232323−2300000000000000000000000000000000000000000000000000000000
χ1078-88-8000000-4000000004-44−434343−434-4-4400000000000000-222-2−232323−2300000000000000000000000000000000000000000000000000000000
χ1088-88-8000000-4000000004-44−434343−43-444-4000000000000002-2-2223−23−232300000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).