Finite Group Databasebeta

← Group #13137440

Character table — Group #13137440

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222224444446666666666666666666612121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order12223444444666121212121212336666661212121212121212121212123666121212121212121212121212121212121212888888882424242424242424242424242424242444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ611111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ711111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ811111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222-1222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ10222222222222222222222-1222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ1122222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1222222222222222222222-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ132222222-2-2-2-222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ142222222-2-2-2-222222-2-2-2-22-1222-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1111100000000000000000000000000000000−i3i3−i3i3
χ152222222-2-2-2-222222-2-2-2-22-1222-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1111100000000000000000000000000000000i3−i3i3−i3
χ162222222-2-2-2-222222-2-2-2-2-12-1-1-1222-1-1-1-111111111-1-1-1-122-2-2-2-21111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−3000000000000
χ172222222-2-2-2-222222-2-2-2-2-12-1-1-1222-1-1-1-111111111-1-1-1-122-2-2-2-21111-1-1-1-1111100000000−3−3−3−33333−3−3−3−33333000000000000
χ1822222-2-222-2-2222-2-222-2-222222222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ1922222-2-222-2-2222-2-222-2-22-1222-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-111-1-11111111111-1-1-1-100000000000000000000000000000000−i3i3i3−i3
χ2022222-2-222-2-2222-2-222-2-22-1222-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-111-1-11111111111-1-1-1-100000000000000000000000000000000i3−i3−i3i3
χ2122222-2-222-2-2222-2-222-2-2-12-1-1-12221111-1-1-1-11111-1-1-1-1-2-222-2-211111111-1-1-1-1000000003333−3−3−3−3−3−3−3−33333000000000000
χ2222222-2-222-2-2222-2-222-2-2-12-1-1-12221111-1-1-1-11111-1-1-1-1-2-222-2-211111111-1-1-1-100000000−3−3−3−333333333−3−3−3−3000000000000
χ2322222-2-2-2-222222-2-2-2-2222-1222-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-11111-1-1-1-1-1-111111111000000000000000000000000002-20000-1-111
χ2422222-2-2-2-222222-2-2-2-2222-1222-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-11111-1-1-1-1-1-11111111100000000000000000000000000-22000011-1-1
χ2522222-2-2-2-222222-2-2-2-222-12-1-1-122211111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ2622222-2-2-2-222222-2-2-2-222-12-1-1-122211111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2722-2-22002-2002-2-2002-200222-2-22-2-2000022-2-2000022-2-2002-2000000000022-2-222−2−222−2−222−2−222−2−222−2−222−2−2000000000000
χ2822-2-22002-2002-2-2002-200222-2-22-2-2000022-2-2000022-2-2002-2000000000022-2-2−2−222−2−222−2−222−2−222−2−222−2−222000000000000
χ2922-2-22002-2002-2-2002-200-12-1112-2-233−3−3-1-11133−3−3-1-111002-20033−3−333−3−3-1-11122−2−222−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ3022-2-22002-2002-2-2002-200-12-1112-2-233−3−3-1-11133−3−3-1-111002-20033−3−333−3−3-1-111−2−222−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3122-2-22002-2002-2-2002-200-12-1112-2-2−3−333-1-111−3−333-1-111002-200−3−333−3−333-1-11122−2−222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3222-2-22002-2002-2-2002-200-12-1112-2-2−3−333-1-111−3−333-1-111002-200−3−333−3−333-1-111−2−222−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ3322-2-2200-22002-2-200-2200222-2-22-2-20000-2-222000022-2-200-220000000000-2-22222−2−2−2−22222−2−222−2−2−2−222−2−222000000000000
χ3422-2-2200-22002-2-200-2200222-2-22-2-20000-2-222000022-2-200-220000000000-2-222−2−22222−2−2−2−222−2−22222−2−222−2−2000000000000
χ3522-2-2200-22002-2-200-2200-12-1112-2-233−3−311-1-1−3−333-1-11100-2200−3−33333−3−311-1-122−2−2−2−222ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ3622-2-2200-22002-2-200-2200-12-1112-2-233−3−311-1-1−3−333-1-11100-2200−3−33333−3−311-1-1−2−22222−2−2−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3722-2-2200-22002-2-200-2200-12-1112-2-2−3−33311-1-133−3−3-1-11100-220033−3−3−3−33311-1-122−2−2−2−222ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ3822-2-2200-22002-2-200-2200-12-1112-2-2−3−33311-1-133−3−3-1-11100-220033−3−3−3−33311-1-1−2−22222−2−2−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ392-22-222-20000-22-22-2000022-22-2-22-22-22-2000000002-22-22-2000000002-22-200002−22−22−22−22−22−22−22−22−22−22−22−2000000000000
χ402-22-222-20000-22-22-2000022-22-2-22-22-22-2000000002-22-22-2000000002-22-20000−22−22−22−22−22−22−22−22−22−22−22−22000000000000
χ412-22-222-20000-22-22-20000-121-11-22-2-11-113−33−33−33−3-11-112-200003−33−3-11-113−33−32−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ422-22-222-20000-22-22-20000-121-11-22-2-11-113−33−33−33−3-11-112-200003−33−3-11-113−33−3−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ432-22-222-20000-22-22-20000-121-11-22-2-11-11−33−33−33−33-11-112-20000−33−33-11-11−33−332−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ442-22-222-20000-22-22-20000-121-11-22-2-11-11−33−33−33−33-11-112-20000−33−33-11-11−33−33−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ452-22-22-220000-22-2-22000022-22-2-22-2-22-22000000002-22-2-2200000000-22-2200002−22−2−22−222−22−22−22−2−22−22−22−22000000000000
χ462-22-22-220000-22-2-22000022-22-2-22-2-22-22000000002-22-2-2200000000-22-220000−22−222−22−2−22−22−22−222−22−22−22−2000000000000
χ472-22-22-220000-22-2-220000-121-11-22-21-11-13−33−3−33−33-11-11-220000−33−331-11-13−33−32−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ482-22-22-220000-22-2-220000-121-11-22-21-11-13−33−3−33−33-11-11-220000−33−331-11-13−33−3−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ492-22-22-220000-22-2-220000-121-11-22-21-11-1−33−333−33−3-11-11-2200003−33−31-11-1−33−332−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ502-22-22-220000-22-2-220000-121-11-22-21-11-1−33−333−33−3-11-11-2200003−33−31-11-1−33−33−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ512-2-22200002-2-2-2200002-222-2-22-2-22000000002-2-222-2-2200002-22-2-22000000002-2-2200002-2-222-2-2200000000000000000000
χ522-2-22200002-2-2-2200002-222-2-22-2-22000000002-2-222-2-2200002-22-2-2200000000-222-20000-222-2-222-200000000000000000000
χ532-2-22200002-2-2-2200002-2-1211-1-2-223−3−33−333−3-111-1-111-100002-2-111-13−3−33−333−32-2-220000-111-1-111-1−333−33−3−33000000000000
χ542-2-22200002-2-2-2200002-2-1211-1-2-223−3−33−333−3-111-1-111-100002-2-111-13−3−33−333−3-222-200001-1-111-1-113−3−33−333−3000000000000
χ552-2-22200002-2-2-2200002-2-1211-1-2-22−333−33−3−33-111-1-111-100002-2-111-1−333−33−3−332-2-220000-111-1-111-13−3−33−333−3000000000000
χ562-2-22200002-2-2-2200002-2-1211-1-2-22−333−33−3−33-111-1-111-100002-2-111-1−333−33−3−33-222-200001-1-111-1-11−333−33−3−33000000000000
χ572-2-2220000-22-2-220000-2222-2-22-2-2200000000-222-22-2-220000-22-222-20000000000002-2-22000000002-2-222-2-22000000000000
χ582-2-2220000-22-2-220000-2222-2-22-2-2200000000-222-22-2-220000-22-222-2000000000000-222-200000000-222-2-222-2000000000000
χ592-2-2220000-22-2-220000-22-1211-1-2-223−3−333−3−331-1-11-111-10000-221-1-113−3−333−3−3300002-2-223−3−33−333−3-111-1-111-1000000000000
χ602-2-2220000-22-2-220000-22-1211-1-2-223−3−333−3−331-1-11-111-10000-221-1-113−3−333−3−330000-222-2−333−33−3−331-1-111-1-11000000000000
χ612-2-2220000-22-2-220000-22-1211-1-2-22−333−3−333−31-1-11-111-10000-221-1-11−333−3−333−300002-2-22−333−33−3−33-111-1-111-1000000000000
χ622-2-2220000-22-2-220000-22-1211-1-2-22−333−3−333−31-1-11-111-10000-221-1-11−333−3−333−30000-222-23−3−33−333−31-1-111-1-11000000000000
χ6344444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2111111111111000000000000000000000000000000000000
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χ6644444-4-4-4-444444-4-4-4-444-2-2-2-2-2-2-2-222222222-2-2-2-211112222-2-21111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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χ794-4-44400004-4-4-4400004-44-2-4-4422-2000000004-4-44-222-20000-22-222-200000000000000000000000000000000000000000000
χ804-4-44400004-4-4-4400004-4-2-222-222-223−23−2323−232323−23-222-21-1-110000-221-1-11−333−33−3−33000000000000000000000000000000000000
χ814-4-44400004-4-4-4400004-4-2-222-222-2−232323−2323−23−2323-222-21-1-110000-221-1-113−3−33−333−3000000000000000000000000000000000000
χ824-4-4440000-44-4-440000-444-2-4-4422-200000000-444-4-222-200002-22-2-2200000000000000000000000000000000000000000000
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χ856666-3666666-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000002200-1-1-1-10000
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χ906666-3-6-666-6-6-3-3-333-3-3330000000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i30000
χ916666-3-6-6-6-666-3-3-33333-3-30000000000000000000000000000000000000000000000000000000000000000002-200-1-1110000
χ926666-3-6-6-6-666-3-3-33333-3-3000000000000000000000000000000000000000000000000000000000000000000-220011-1-10000
χ931212-12-12-60012-1200-66600-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ941212-12-12-600-121200-666006-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-1212-12-612-1200006-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-12-6-121200006-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-6000012-1266-60000-66000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-60000-121266-600006-6000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.