Finite Group Databasebeta

← Group #13139021

Character table — Group #13139021

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order124423468888121224242424612242433666612121212121224242424366661212121212242424242424242424242424242422444466668888881212121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ511111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ711111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ811111111-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111
χ911-1-1-1111ii−i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1ii−i−i1-1-1-11111-1-1ii−i−ii−iiiii−i−i−i−i11-1-1i−i1111i−ii−i1-1-1-1ii−i−i-1-1ii−i−i11-1-1ii−i−i
χ1011-1-1-1111ii−i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1ii−i−i1-1-1-11111-1-1ii−i−ii−iiiii−i−i−i−i1-1-11−ii11-1-1i−i−ii-11-1-1−i−iii11ii−i−i-1-111−i−iii
χ1111-1-1-1111ii−i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1ii−i−i1-1-1-11111-1-1ii−i−ii−iiiii−i−i−i−i-111-1−ii-1-111−iii−i-1111−i−iii-1-1−i−iii-1-111ii−i−i
χ1211-1-1-1111ii−i−i-1-1ii−i−i-11i−i111-1-11-1-111-1-1ii−i−i1-1-1-11111-1-1ii−i−ii−iiiii−i−i−i−i-1-111i−i-1-1-1-1−ii−ii1-111ii−i−i11−i−iii11-1-1−i−iii
χ1311-1-1-1111−i−iii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−iii1-1-1-11111-1-1−i−iii−ii−i−i−i−iiiii11-1-1−ii1111−ii−ii1-1-1-1−i−iii-1-1−i−iii11-1-1−i−iii
χ1411-1-1-1111−i−iii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−iii1-1-1-11111-1-1−i−iii−ii−i−i−i−iiiii1-1-11i−i11-1-1−iii−i-11-1-1ii−i−i11−i−iii-1-111ii−i−i
χ1511-1-1-1111−i−iii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−iii1-1-1-11111-1-1−i−iii−ii−i−i−i−iiiii-111-1i−i-1-111i−i−ii-1111ii−i−i-1-1ii−i−i-1-111−i−iii
χ1611-1-1-1111−i−iii-1-1−i−iii-11−ii111-1-11-1-111-1-1−i−iii1-1-1-11111-1-1−i−iii−ii−i−i−i−iiiii-1-111−ii-1-1-1-1i−ii−i1-111−i−iii11ii−i−i11-1-1ii−i−i
χ1722222222222222222222222-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-102020000-1-1002200000000-1-100000000-1-1-1-1
χ1822222222222222222222222-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10-20-200001100-2-20000000011000000001111
χ192222222222222222222222-12-1-1-12-1-1-1-1222222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022000000002200-1-1-1-1000000-1-1-1-10000
χ202222222222222222222222-12-1-1-12-1-1-1-1222222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-200000000-2-200111100000011110000
χ2122222222-2-2-2-222-2-2-2-222-2-22-1222-12222-1-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111102020000-1-100-2-200000000-1-1000000001111
χ2222222222-2-2-2-222-2-2-2-222-2-22-1222-12222-1-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111110-20-20000110022000000001100000000-1-1-1-1
χ2322222222-2-2-2-222-2-2-2-222-2-2-12-1-1-12-1-1-1-122-2-2-2-2-12-1-1-12-1-1-1-11111-2-21111111100002200000000-2-200-1-1-1-100000011110000
χ2422222222-2-2-2-222-2-2-2-222-2-2-12-1-1-12-1-1-1-122-2-2-2-2-12-1-1-12-1-1-1-11111-2-2111111110000-2-20000000022001111000000-1-1-1-10000
χ252222-22-222-22-2222222-2-2-2-2222-2-2222-2-222-2-2-2-22-2-2-22-2-2-2222-22-22222-2-222-2-2000000000000000000000000000000000000
χ262222-22-222-22-2222222-2-2-2-22-12-2-2-122-2-2-1-11111-1111-1111-1-12-22-2-1-1-1-111-1-11100000000−i3i3000000000000−i3i300000000−i3i3−i3i3
χ272222-22-222-22-2222222-2-2-2-22-12-2-2-122-2-2-1-11111-1111-1111-1-12-22-2-1-1-1-111-1-11100000000i3−i3000000000000i3−i300000000i3−i3i3−i3
χ282222-22-222-22-2222222-2-2-2-2-12-1112-1-11122-2-2-2-2-1-211-1-211-1-1-11-1122-1-111-1-1110000000000000000003−33−30000003−33−30000
χ292222-22-222-22-2222222-2-2-2-2-12-1112-1-11122-2-2-2-2-1-211-1-211-1-1-11-1122-1-111-1-111000000000000000000−33−33000000−33−330000
χ302222-22-22-22-2222-2-2-2-2-2-222222-2-2222-2-22222222-2-2-22-2-2-222-22-22-2-2-2-222-2-222000000000000000000000000000000000000
χ312222-22-22-22-2222-2-2-2-2-2-2222-12-2-2-122-2-2-1-1-1-1-1-1-1111-1111-1-1-22-221111-1-111-1-100000000−i3i3000000000000−i3i300000000i3−i3i3−i3
χ322222-22-22-22-2222-2-2-2-2-2-2222-12-2-2-122-2-2-1-1-1-1-1-1-1111-1111-1-1-22-221111-1-111-1-100000000i3−i3000000000000i3−i300000000−i3i3−i3i3
χ332222-22-22-22-2222-2-2-2-2-2-222-12-1112-1-111222222-1-211-1-211-1-11-11-1-2-211-1-111-1-10000000000000000003−33−3000000−33−330000
χ342222-22-22-22-2222-2-2-2-2-2-222-12-1112-1-111222222-1-211-1-211-1-11-11-1-2-211-1-111-1-1000000000000000000−33−330000003−33−30000
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χ3622-2-222-222i−2i−2i2i-2-22i2i−2i−2i2-2−2i2i2-1222-1-2-2-2-211ii−i−i-1-1-1-1-1111112i−2i−2i2i−ii−i−iiiii−i−i00000000−i3i3000000000000i3−i3000000003−3−33
χ3722-2-222-222i−2i−2i2i-2-22i2i−2i−2i2-2−2i2i2-1222-1-2-2-2-211ii−i−i-1-1-1-1-1111112i−2i−2i2i−ii−i−iiiii−i−i00000000i3−i3000000000000−i3i300000000−333−3
χ3822-2-222-222i−2i−2i2i-2-22i2i−2i−2i2-2−2i2i-12-1-1-121111-2-2−2i−2i2i2i-12-1-1-1-21111−iii−i2i−2i−i−iiiii−i−i000000000000000000−i3i3i3−i3000000−333−30000
χ3922-2-222-222i−2i−2i2i-2-22i2i−2i−2i2-2−2i2i-12-1-1-121111-2-2−2i−2i2i2i-12-1-1-1-21111−iii−i2i−2i−i−iiiii−i−i000000000000000000i3−i3−i3i30000003−3−330000
χ4022-2-222-22−2i2i2i−2i-2-2−2i−2i2i2i2-22i−2i222222-2-2-2-2-2-22i2i−2i−2i22222-2-2-2-2-2−2i2i2i−2i−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4122-2-222-22−2i2i2i−2i-2-2−2i−2i2i2i2-22i−2i2-1222-1-2-2-2-211−i−iii-1-1-1-1-111111−2i2i2i−2ii−iii−i−i−i−iii00000000−i3i3000000000000i3−i300000000−333−3
χ4222-2-222-22−2i2i2i−2i-2-2−2i−2i2i2i2-22i−2i2-1222-1-2-2-2-211−i−iii-1-1-1-1-111111−2i2i2i−2ii−iii−i−i−i−iii00000000i3−i3000000000000−i3i3000000003−3−33
χ4322-2-222-22−2i2i2i−2i-2-2−2i−2i2i2i2-22i−2i-12-1-1-121111-2-22i2i−2i−2i-12-1-1-1-21111i−i−ii−2i2iii−i−i−i−iii000000000000000000−i3i3i3−i30000003−3−330000
χ4422-2-222-22−2i2i2i−2i-2-2−2i−2i2i2i2-22i−2i-12-1-1-121111-2-22i2i−2i−2i-12-1-1-1-21111i−i−ii−2i2iii−i−i−i−iii000000000000000000i3−i3−i3i3000000−333−30000
χ4522-2-2-22222i2i−2i−2i-2-22i2i−2i−2i-222i−2i2-12-2-2-1-2-22211−i−iii-1111-1-1-1-1112i2i−2i−2i−ii−i−i−i−iiiii020-20000-1-1002i−2i000000001100000000−i−iii
χ4622-2-2-22222i2i−2i−2i-2-22i2i−2i−2i-222i−2i2-12-2-2-1-2-22211−i−iii-1111-1-1-1-1112i2i−2i−2i−ii−i−i−i−iiiii0-20200001100−2i2i00000000-1-100000000ii−i−i
χ4722-2-2-22222i2i−2i−2i-2-22i2i−2i−2i-222i−2i-12-111211-1-1-2-22i2i−2i−2i-1-211-12-1-111−i−iii2i−2i−i−i−i−iiiii00002i−2i000000002-200−i−iii000000-1-1110000
χ4822-2-2-22222i2i−2i−2i-2-22i2i−2i−2i-222i−2i-12-111211-1-1-2-22i2i−2i−2i-1-211-12-1-111−i−iii2i−2i−i−i−i−iiiii0000−2i2i00000000-2200ii−i−i00000011-1-10000
χ4922-2-2-2222−2i−2i2i2i-2-2−2i−2i2i2i-22−2i2i2-12-2-2-1-2-22211ii−i−i-1111-1-1-1-111−2i−2i2i2ii−iiiii−i−i−i−i020-20000-1-100−2i2i000000001100000000ii−i−i
χ5022-2-2-2222−2i−2i2i2i-2-2−2i−2i2i2i-22−2i2i2-12-2-2-1-2-22211ii−i−i-1111-1-1-1-111−2i−2i2i2ii−iiiii−i−i−i−i0-202000011002i−2i00000000-1-100000000−i−iii
χ5122-2-2-2222−2i−2i2i2i-2-2−2i−2i2i2i-22−2i2i-12-111211-1-1-2-2−2i−2i2i2i-1-211-12-1-111ii−i−i−2i2iiiii−i−i−i−i00002i−2i00000000-2200−i−iii00000011-1-10000
χ5222-2-2-2222−2i−2i2i2i-2-2−2i−2i2i2i-22−2i2i-12-111211-1-1-2-2−2i−2i2i2i-1-211-12-1-111ii−i−i−2i2iiiii−i−i−i−i0000−2i2i000000002-200ii−i−i000000-1-1110000
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χ5444444444-4-4-4-444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2111-21111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-44-444-44-4444444-4-4-4-4-2-2-222-2-2-222-2-2222212-1-112-1-111-22-22-2-211-1-111-1-1000000000000000000000000000000000000
χ564444-44-44-44-4444-4-4-4-4-4-444-2-2-222-2-2-222-2-2-2-2-2-212-1-112-1-1112-22-222-1-111-1-111000000000000000000000000000000000000
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χ8166666-36-3-6-6-6-6-3-33333-3-3330000000000000000000000000000000000000000202000-1-100-2-20000-1-1000000111100000000
χ8266666-36-3-6-6-6-6-3-33333-3-3330000000000000000000000000000000000000000-20-2000110022000011000000-1-1-1-100000000
χ836666-6-3-6-36-66-6-3-3-3-3-3-333330000000000000000000000000000000000000000000000−i3i300000000−i3i3000000−i3i3−i3i300000000
χ846666-6-3-6-36-66-6-3-3-3-3-3-333330000000000000000000000000000000000000000000000i3−i300000000i3−i3000000i3−i3i3−i300000000
χ856666-6-3-6-3-66-66-3-3333333-3-30000000000000000000000000000000000000000000000−i3i300000000−i3i3000000i3−i3i3−i300000000
χ866666-6-3-6-3-66-66-3-3333333-3-30000000000000000000000000000000000000000000000i3−i300000000i3−i3000000−i3i3−i3i300000000
χ8766-6-66-3-6-36i−6i−6i6i33−3i−3i3i3i-333i−3i0000000000000000000000000000000000000000000000−i3i300000000i3−i30000003−3−3300000000
χ8866-6-66-3-6-36i−6i−6i6i33−3i−3i3i3i-333i−3i0000000000000000000000000000000000000000000000i3−i300000000−i3i3000000−333−300000000
χ8966-6-66-3-6-3−6i6i6i−6i333i3i−3i−3i-33−3i3i0000000000000000000000000000000000000000000000−i3i300000000i3−i3000000−333−300000000
χ9066-6-66-3-6-3−6i6i6i−6i333i3i−3i−3i-33−3i3i0000000000000000000000000000000000000000000000i3−i300000000−i3i30000003−3−3300000000
χ9166-6-6-6-36-36i6i−6i−6i33−3i−3i3i3i3-3−3i3i000000000000000000000000000000000000000020-2000-1-1002i−2i000011000000−i−iii00000000
χ9266-6-6-6-36-36i6i−6i−6i33−3i−3i3i3i3-3−3i3i0000000000000000000000000000000000000000-2020001100−2i2i0000-1-1000000ii−i−i00000000
χ9366-6-6-6-36-3−6i−6i6i6i333i3i−3i−3i3-33i−3i000000000000000000000000000000000000000020-2000-1-100−2i2i000011000000ii−i−i00000000
χ9466-6-6-6-36-3−6i−6i6i6i333i3i−3i−3i3-33i−3i0000000000000000000000000000000000000000-20200011002i−2i0000-1-1000000−i−iii00000000
χ9512-1212i−12i0-6060000−6i6i−6ζ7+6ζ236ζ7−6ζ236ζ5−6ζ13−6ζ5+6ζ1300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212i−12i0-6060000−6i6i6ζ7−6ζ23−6ζ7+6ζ23−6ζ5+6ζ136ζ5−6ζ1300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12−12i12i0-60600006i−6i6ζ5−6ζ13−6ζ5+6ζ13−6ζ7+6ζ236ζ7−6ζ2300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12−12i12i0-60600006i−6i−6ζ5+6ζ136ζ5−6ζ136ζ7−6ζ23−6ζ7+6ζ2300000000000000000000000000000000000000000000000000000000000000000000000000000000

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