Finite Group Databasebeta

← Group #13140038

Character table — Group #13140038

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122222222222222222222226666666612121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818727272727272727272727272
order122222344446666666121212121212121233666666366666666666121212121212121212121212121212128888888824242424242424242424242424242424244466121212121212
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
χ51111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ61111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ71111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111
χ81111-1-111-1-1111-1-1-1-1111-1-1-1-111111111111-1-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1
χ9222222222222222222222222222-12-1-12-12-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000000000002200-1-1-1-10000
χ10222222222222222222222222222-12-1-12-12-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000-2-20011110000
χ1122222222222222222222222222-12-122-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000220000-1-1-1-1
χ1222222222222222222222222222-12-122-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-200001111
χ132222222-2-2-2-22222222-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ142222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-1-12-12-122-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000000000000000000000000000−i3i3−i3i30000
χ152222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-1-12-12-122-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000000000000000000000000000i3−i3i3−i30000
χ162222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-122-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000000000000000−i3i3−i3i3
χ172222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-122-12-1-1-1-122-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000000000000000000i3−i3i3−i3
χ182222-2-222-2-2222-2-2-2-2222-2-2-2-2222-12-1-12-12-1-2-211-1-11111-1-1-11122-2-2-1-1-1-111110000000000000000000000002-200-1-1110000
χ192222-2-222-2-2222-2-2-2-2222-2-2-2-2222-12-1-12-12-1-2-211-1-11111-1-1-11122-2-2-1-1-1-11111000000000000000000000000-220011-1-10000
χ202222-2-222-2-2222-2-2-2-2222-2-2-2-222-12-122-12-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-11111000000000000000000000000002-20000-1-111
χ212222-2-222-2-2222-2-2-2-2222-2-2-2-222-12-122-12-1-111-2-2-1-11111-122-2-2-1-111-1-1-1-1111100000000000000000000000000-22000011-1-1
χ222222-2-22-222-222-2-2-2-22-2-22222-2-2222222222-2-2-2-222-2-2-2-22-2-222-2-222-2-2-2-22222000000000000000000000000000000000000
χ232222-2-22-222-222-2-2-2-22-2-22222-2-22-12-1-12-12-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-10000000000000000000000000000−i3i3i3−i30000
χ242222-2-22-222-222-2-2-2-22-2-22222-2-22-12-1-12-12-1-2-211-1-11111-111-1-1-2-2221111-1-1-1-10000000000000000000000000000i3−i3−i3i30000
χ252222-2-22-222-222-2-2-2-22-2-22222-2-2-12-122-12-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-100000000000000000000000000000000−i3i3i3−i3
χ262222-2-22-222-222-2-2-2-22-2-22222-2-2-12-122-12-1-111-2-2-1-11111-1-2-22211-1-11111-1-1-1-100000000000000000000000000000000i3−i3−i3i3
χ2722-2-200202i−2i02-20000-2002i2i−2i−2i0022-22-22-2-2200002-20000-2002i−2i002i−2i00002i2i−2i−2i22−2−2−i2−i2i2i22222−2−2−2−2−i2−i2−i2−i2i2i2i2i2000000000000
χ2822-2-200202i−2i02-20000-2002i2i−2i−2i0022-22-22-2-2200002-20000-2002i−2i002i−2i00002i2i−2i−2i−2−222i2i2−i2−i2−2−2−2−22222i2i2i2i2−i2−i2−i2−i2000000000000
χ2922-2-20020−2i2i02-20000-200−2i−2i2i2i0022-22-22-2-2200002-20000-200−2i2i00−2i2i0000−2i−2i2i2i22−2−2i2i2−i2−i22222−2−2−2−2i2i2i2i2−i2−i2−i2−i2000000000000
χ3022-2-20020−2i2i02-20000-200−2i−2i2i2i0022-22-22-2-2200002-20000-200−2i2i00−2i2i0000−2i−2i2i2i−2−222−i2−i2i2i2−2−2−2−22222−i2−i2−i2−i2i2i2i2i2000000000000
χ312-22-22-220000-2222-2-2-200000000222-2-2-22-222-22-2-2222-2-2-20000000000000000−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ322-22-22-220000-2222-2-2-200000000222-2-2-22-222-22-2-2222-2-2-20000000000000000i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ332-22-2-2220000-22-2-222-200000000222-2-2-22-22-22-22-22-2-222-20000000000000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ342-22-2-2220000-22-2-222-200000000222-2-2-22-22-22-22-22-2-222-20000000000000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ352-2-22002200-2-2-200002220000-2-222-2-22-2-2220000-2-2000022-2002-20022-2-200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362-2-22002200-2-2-200002220000-2-222-2-22-2-2220000-2-2000022-2002-20022-2-20000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372-2-22002-2002-2-200002-2-200002222-2-22-2-2220000-2-200002-2200-2200-2-222000000002-2-220000000022-2-2-2-222000000000000
χ382-2-22002-2002-2-200002-2-200002222-2-22-2-2220000-2-200002-2200-2200-2-22200000000-222-200000000-2-22222-2-2000000000000
χ3944444444444444444444444444-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ404444444-4-4-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-21-2-2-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ414444-4-444-4-4444-4-4-4-4444-4-4-4-444-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000
χ424444-4-44-444-444-4-4-4-44-4-44444-4-4-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ4344-4-400404i−4i04-40000-4004i4i−4i−4i004-2-4-2242-4-20000-220000200−2i2i004i−4i0000−2i−2i2i2i000000000000000000000000000000000000
χ4444-4-400404i−4i04-40000-4004i4i−4i−4i00-2424-4-2-42-20000-2200002004i−4i00−2i2i0000−2i−2i2i2i000000000000000000000000000000000000
χ4544-4-400404i−4i04-40000-4004i4i−4i−4i00-2-22-22-222100001-13-33-3-100−2i2i00−2i2i3i−3i3i−3iii−i−i000000000000000000000000000000000000
χ4644-4-400404i−4i04-40000-4004i4i−4i−4i00-2-22-22-222100001-1-33-33-100−2i2i00−2i2i−3i3i−3i3iii−i−i000000000000000000000000000000000000
χ4744-4-40040−4i4i04-40000-400−4i−4i4i4i004-2-4-2242-4-20000-2200002002i−2i00−4i4i00002i2i−2i−2i000000000000000000000000000000000000
χ4844-4-40040−4i4i04-40000-400−4i−4i4i4i00-2424-4-2-42-20000-220000200−4i4i002i−2i00002i2i−2i−2i000000000000000000000000000000000000
χ4944-4-40040−4i4i04-40000-400−4i−4i4i4i00-2-22-22-222100001-13-33-3-1002i−2i002i−2i−3i3i−3i3i−i−iii000000000000000000000000000000000000
χ5044-4-40040−4i4i04-40000-400−4i−4i4i4i00-2-22-22-222100001-1-33-33-1002i−2i002i−2i3i−3i3i−3i−i−iii000000000000000000000000000000000000
χ514-44-44-440000-4444-4-4-4000000004-2422-4-2-4-24-4-222-2-2-22220000000000000000000000000000000000000000000000000000
χ524-44-44-440000-4444-4-4-400000000-24-2-4-4242-2-224-42-2-2-22220000000000000000000000000000000000000000000000000000
χ534-44-44-440000-4444-4-4-400000000-2-2-2222-221-22-22-1111-1-1-1000000003i−3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ544-44-44-440000-4444-4-4-400000000-2-2-2222-221-22-22-1111-1-1-100000000−3i3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ554-44-4-4440000-44-4-444-4000000004-2422-4-2-4-2-442-22-222-2-220000000000000000000000000000000000000000000000000000
χ564-44-4-4440000-44-4-444-400000000-24-2-4-4242-22-2-442-222-2-220000000000000000000000000000000000000000000000000000
χ574-44-4-4440000-44-4-444-400000000-2-2-2222-2212-22-2-11-1-111-1000000003i−3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
χ584-44-4-4440000-44-4-444-400000000-2-2-2222-2212-22-2-11-1-111-100000000−3i3i3i−3i3i−3i3i−3i000000000000000000000000000000000000
χ594-4-44004400-4-4-400004440000-4-44-2-42-2-424-20000220000-2-22004-400-2-2220000000000000000000000000000000000000000
χ604-4-44004400-4-4-400004440000-4-4-242-442-4-2-20000220000-24-400-2200-2-2220000000000000000000000000000000000000000
χ614-4-44004400-4-4-400004440000-4-4-2-222-222-210000-1-13-3-331-2200-220011-1-13-3-33000000000000000000000000000000000000
χ624-4-44004400-4-4-400004440000-4-4-2-222-222-210000-1-1-333-31-2200-220011-1-1-333-3000000000000000000000000000000000000
χ634-4-44004-4004-4-400004-4-40000444-2-42-2-424-20000220000-22-200-440022-2-20000000000000000000000000000000000000000
χ644-4-44004-4004-4-400004-4-4000044-242-442-4-2-20000220000-2-44002-20022-2-20000000000000000000000000000000000000000
χ654-4-44004-4004-4-400004-4-4000044-2-222-222-210000-1-13-3-3312-2002-200-1-111-333-3000000000000000000000000000000000000
χ664-4-44004-4004-4-400004-4-4000044-2-222-222-210000-1-1-333-312-2002-200-1-1113-3-33000000000000000000000000000000000000
χ67666666-36666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ68666666-36666-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000-2-2-2-2-2-2-2-21111111111111111000000000000
χ69666666-3-6-6-6-6-3-3-3-3-3-3-333333333000000000000000000000000000000000000000000003−33−33−33−33−33−33−33−3000000000000
χ70666666-3-6-6-6-6-3-3-3-3-3-3-33333333300000000000000000000000000000000000000000000−33−33−33−33−33−33−33−33000000000000
χ716666-6-6-36-6-66-3-33333-3-3-33333-3-30000000000000000000000000000000000002222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ726666-6-6-36-6-66-3-33333-3-3-33333-3-3000000000000000000000000000000000000-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ736666-6-6-3-666-6-3-33333-333-3-3-3-333000000000000000000000000000000000000000000003−33−33−33−3−33−33−33−33000000000000
χ746666-6-6-3-666-6-3-33333-333-3-3-3-33300000000000000000000000000000000000000000000−33−33−33−333−33−33−33−3000000000000
χ7566-6-600-306i−6i0-33−3i33i3−3i33i3333−33−3i−3i3i3i33−3300000000000000000000000000000000000022−2−2−i2−i2i2i2ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ7666-6-600-306i−6i0-33−3i33i3−3i33i3333−33−3i−3i3i3i33−33000000000000000000000000000000000000−2−222i2i2−i2−i2−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23000000000000
χ7766-6-600-306i−6i0-333i3−3i33i3−3i33−3333−3i−3i3i3i−333300000000000000000000000000000000000022−2−2−i2−i2i2i2ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ7866-6-600-306i−6i0-333i3−3i33i3−3i33−3333−3i−3i3i3i−3333000000000000000000000000000000000000−2−222i2i2−i2−i2−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7000000000000
χ7966-6-600-30−6i6i0-33−3i33i3−3i33i33−33333i3i−3i−3i−333300000000000000000000000000000000000022−2−2i2i2−i2−i2ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7000000000000
χ8066-6-600-30−6i6i0-33−3i33i3−3i33i33−33333i3i−3i−3i−3333000000000000000000000000000000000000−2−222−i2−i2i2i2−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7000000000000
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χ8266-6-600-30−6i6i0-333i3−3i33i3−3i3333−333i3i−3i−3i33−33000000000000000000000000000000000000−2−222−i2−i2i2i2−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23000000000000
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χ886-66-6-66-300003-333-3-3333−33−3333−3333−3333000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
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χ906-66-6-66-300003-333-3-33−333333−3333−3333−33000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
χ916-6-6600-3600-633−3i33i33i3−3i3-3-3-3−3i33i33i3−3i3330000000000000000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i−333−33−3−33000000000000
χ926-6-6600-3600-633−3i33i33i3−3i3-3-3-3−3i33i33i3−3i333000000000000000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii3−3−33−333−3000000000000
χ936-6-6600-3600-6333i3−3i3−3i33i3-3-3-33i3−3i3−3i33i3330000000000000000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i3−3−33−333−3000000000000
χ946-6-6600-3600-6333i3−3i3−3i33i3-3-3-33i3−3i3−3i33i333000000000000000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii−333−33−3−33000000000000
χ956-6-6600-3-600633−3i33i33i3−3i3-3333i3−3i3−3i33i3-3-300000000000000000000000000000000000000002-2-22i3−i3−i3i3−i3i3i3−i3-1-11111-1-1000000000000
χ966-6-6600-3-600633−3i33i33i3−3i3-3333i3−3i3−3i33i3-3-30000000000000000000000000000000000000000-222-2−i3i3i3−i3i3−i3−i3i311-1-1-1-111000000000000
χ976-6-6600-3-6006333i3−3i3−3i33i3-333−3i33i33i3−3i3-3-300000000000000000000000000000000000000002-2-22−i3i3i3−i3i3−i3−i3i3-1-11111-1-1000000000000
χ986-6-6600-3-6006333i3−3i3−3i33i3-333−3i33i33i3−3i3-3-30000000000000000000000000000000000000000-222-2i3−i3−i3i3−i3i3i3−i311-1-1-1-111000000000000

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