Finite Group Databasebeta

← Group #10701748

Character table — Group #10701748

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222222222222366666666666666644444444666666661212121212121212121212121212121244444444121212121212121212121212121212122222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ23222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ24222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ2522222222-2-2-2-222-2-222-2-2222222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2622222222-2-2-2-222-2-222-2-22222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2722222222-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222222-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222222-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3022222222-2-2-2-222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3122222222-2-2-2-2-2-222-2-2222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ3222222222-2-2-2-2-2-222-2-2222222222-2-2-2-2-2-2-2-22-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ3322222222-2-2-2-2-2-222-2-222-1-1-1-1-1-1-111111111-122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-2-222-2-222-1-1-1-1-1-1-111111111-122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-2-222-2-222-1-1-1-1-1-1-111111111-1-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-2-222-2-222-1-1-1-1-1-1-111111111-1-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ37222-2-2-2-2222-2-2222-2-2-22-22222-2-2-22222-2-2-2-2-20000000022-2-222-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ38222-2-2-2-2222-2-2222-2-2-22-22222-2-2-22222-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ39222-2-2-2-2222-2-2-2-2-2222-222222-2-2-2-2-2-2-22222-20000000022-2-2-2-22200000000000000000000000000000000000000000000000000002-2-22
χ40222-2-2-2-2222-2-2-2-2-2222-222222-2-2-2-2-2-2-22222-20000000022-2-2-2-2220000000000000000000000000000000000000000000000000000-222-2
χ41222-2-2-2-22-2-22222-22-2-2-222222-2-2-22222-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ42222-2-2-2-22-2-22222-22-2-2-222222-2-2-22222-2-2-2-2-200000000-2-222-2-222000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ43222-2-2-2-22-2-222-2-22-2222-22222-2-2-2-2-2-2-22222-200000000-2-22222-2-20000000000000000000000000000000000000000000000002-2-220000
χ44222-2-2-2-22-2-222-2-22-2222-22222-2-2-2-2-2-2-22222-200000000-2-22222-2-2000000000000000000000000000000000000000000000000-222-20000
χ452-2-222-2-222-22-22-2222-2-2-222-2-222-222-2-222-2-2-2000000002-22-22-22-2000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-2-222-2-222-22-22-2222-2-2-222-2-222-222-2-222-2-2-2000000002-22-22-22-200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-2-222-2-222-22-22-2222-2-2-2-1-111-1-11-1-111-1-111100000000-11-11-11-1133−3−333−3−333−3−333−3−300002i−2i2i−2i−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii0000000000000000
χ482-2-222-2-222-22-22-2222-2-2-2-1-111-1-11-1-111-1-111100000000-11-11-11-1133−3−333−3−333−3−333−3−30000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i0000000000000000
χ492-2-222-2-222-22-22-2222-2-2-2-1-111-1-11-1-111-1-111100000000-11-11-11-11−3−333−3−333−3−333−3−33300002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii0000000000000000
χ502-2-222-2-222-22-22-2222-2-2-2-1-111-1-11-1-111-1-111100000000-11-11-11-11−3−333−3−333−3−333−3−3330000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i0000000000000000
χ512-2-222-2-222-22-2-22-2-2-222222-2-222-2-2-222-2-222-2000000002-22-2-22-22000000000000000000002-2-22000000002-22-2-22-220000000000000000
χ522-2-222-2-222-22-2-22-2-2-222222-2-222-2-2-222-2-222-2000000002-22-2-22-2200000000000000000000-222-200000000-22-222-22-20000000000000000
χ532-2-222-2-222-22-2-22-2-2-2222-1-111-1-1111-1-111-1-1100000000-11-111-11-133−3−333−3−3−3−333−3−33300002-2-22−33−333−33−3-11-111-11-10000000000000000
χ542-2-222-2-222-22-2-22-2-2-2222-1-111-1-1111-1-111-1-1100000000-11-111-11-133−3−333−3−3−3−333−3−3330000-222-23−33−3−33−331-11-1-11-110000000000000000
χ552-2-222-2-222-22-2-22-2-2-2222-1-111-1-1111-1-111-1-1100000000-11-111-11-1−3−333−3−33333−3−333−3−300002-2-223−33−3−33−33-11-111-11-10000000000000000
χ562-2-222-2-222-22-2-22-2-2-2222-1-111-1-1111-1-111-1-1100000000-11-111-11-1−3−333−3−33333−3−333−3−30000-222-2−33−333−33−31-11-1-11-110000000000000000
χ572-2-222-2-22-22-222-2-2-22-22222-2-222-222-2-222-2-2-200000000-22-22-22-2200000000000000002-22-200002-2-222-2-22000000000000000000000000
χ582-2-222-2-22-22-222-2-2-22-22222-2-222-222-2-222-2-2-200000000-22-22-22-220000000000000000-22-220000-222-2-222-2000000000000000000000000
χ592-2-222-2-22-22-222-2-2-22-222-1-111-1-11-1-111-1-1111000000001-11-11-11-133−3−3−3−33333−3−3−3−3332-22-20000-111-1-111-13−3−333−3−330000000000000000
χ602-2-222-2-22-22-222-2-2-22-222-1-111-1-11-1-111-1-1111000000001-11-11-11-133−3−3−3−33333−3−3−3−333-22-2200001-1-111-1-11−333−3−333−30000000000000000
χ612-2-222-2-22-22-222-2-2-22-222-1-111-1-11-1-111-1-1111000000001-11-11-11-1−3−33333−3−3−3−33333−3−32-22-20000-111-1-111-1−333−3−333−30000000000000000
χ622-2-222-2-22-22-222-2-2-22-222-1-111-1-11-1-111-1-1111000000001-11-11-11-1−3−33333−3−3−3−33333−3−3-22-2200001-1-111-1-113−3−333−3−330000000000000000
χ632-2-222-2-22-22-22-2222-22-2-222-2-222-2-2-222-2-222-200000000-22-222-22-200000000000000002i−2i−2i2i00002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ642-2-222-2-22-22-22-2222-22-2-222-2-222-2-2-222-2-222-200000000-22-222-22-20000000000000000−2i2i2i−2i0000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ652-2-222-2-22-22-22-2222-22-2-2-1-111-1-1111-1-111-1-11000000001-11-1-11-1133−3−3−3−333−3−33333−3−32i−2i−2i2i0000−iii−ii−i−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ662-2-222-2-22-22-22-2222-22-2-2-1-111-1-1111-1-111-1-11000000001-11-1-11-1133−3−3−3−333−3−33333−3−3−2i2i2i−2i0000i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ672-2-222-2-22-22-22-2222-22-2-2-1-111-1-1111-1-111-1-11000000001-11-1-11-11−3−33333−3−333−3−3−3−3332i−2i−2i2i0000−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ682-2-222-2-22-22-22-2222-22-2-2-1-111-1-1111-1-111-1-11000000001-11-1-11-11−3−33333−3−333−3−3−3−333−2i2i2i−2i0000i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ692-2-2-2-22222-2-222-22-2-22-2222-2-2-2-2222-2-2-2-2222000000002-2-222-2-2200000000000000000000000000000000000000002-2002-20000000000
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χ9244-4-44-44-4000000000000-22-222-222i3−2i32i3−2i3−2i32i3−2i32i3-2-44000000000000002-22-20000−2i32i3−2i32i300000000000000000000000000000000000000000000
χ934-444-4-44-40000000000004-4-444-4-4000000004004-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ944-444-4-44-40000000000004-4-444-4-400000000400-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ954-444-4-44-4000000000000-222-2-222−2i32i32i3−2i3−2i32i32i3−2i3-2004-40000000000000000-222-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ964-444-4-44-4000000000000-222-2-222−2i32i32i3−2i3−2i32i32i3−2i3-200-4400000000000000002-2-2200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ974-444-4-44-4000000000000-222-2-2222i3−2i3−2i32i32i3−2i3−2i32i3-2004-40000000000000000-222-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ984-444-4-44-4000000000000-222-2-2222i3−2i3−2i32i32i3−2i3−2i32i3-200-4400000000000000002-2-220000−2i32i32i3−2i30000000000000000000000000000000000000000
χ994-44-444-4-40000000000004-4-44-44400000000-400004i−4i0000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ1004-44-444-4-40000000000004-4-44-44400000000-40000−4i4i000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ1014-44-444-4-4000000000000-222-22-2-2−2i32i32i3−2i32i3−2i3−2i32i3200004i−4i000000000023−23−23230000−2i2i2i−2i00000000000000000000000000000000000000000000
χ1024-44-444-4-4000000000000-222-22-2-2−2i32i32i3−2i32i3−2i3−2i32i320000−4i4i0000000000−232323−2300002i−2i−2i2i00000000000000000000000000000000000000000000
χ1034-44-444-4-4000000000000-222-22-2-22i3−2i3−2i32i3−2i32i32i3−2i3200004i−4i0000000000−232323−230000−2i2i2i−2i00000000000000000000000000000000000000000000
χ1044-44-444-4-4000000000000-222-22-2-22i3−2i3−2i32i3−2i32i32i3−2i320000−4i4i000000000023−23−232300002i−2i−2i2i00000000000000000000000000000000000000000000
χ1054-4-4-4-44444-4-444-44-4-44-44-2-22222-2-2-22222-2-2-200000000-222-2-222-200000000000000000000000000000000000000000000000000000000
χ1064-4-4-4-44444-4-44-44-444-44-4-2-22222-222-2-2-2-222-200000000-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4-4444-444-44-4-44-444-4-2-22222-2-2-22222-2-2-2000000002-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4-4444-444-4-444-44-4-44-2-22222-222-2-2-2-222-2000000002-2-22-222-200000000000000000000000000000000000000000000000000000000

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