Finite Group Databasebeta

← Group #72343929

Character table — Group #72343929

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11111111446666888812121212121212121212121212121616242424242424242424242424242432323232323232324848484848484848484848484848484848484848484864646464646464646464646496969696
order122244448822442244222244448888888822224444444488366612121212444444448888888888888866121224242424242424244488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1
χ311111111111111-1-1-1-111111111111111-1-111-1-111-1-111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ711111111-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ811111111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-1-1-1i−i11-1-111-1-11-11-11-11-1iii−i−i−ii−i1111-1-1-1-111-1-1i−i1111-1-1-1-11-11-1ii−i−ii−ii−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−i1-1i−i
χ101111-1-1-1-1i−i11-1-111-1-11-11-11-11-1iii−i−i−ii−i-1-1-1-11111-1-111i−i1111-1-1-1-11-1-11−i−iii−ii−ii−iii−i−ii-1-11111-1-1ii−i−iii−i−i-11−ii
χ111111-1-1-1-1i−i11-1-1-1-1111-11-11-11-1iii−i−i−i−ii11-1-1-1-11111-1-1i−i1111-1-1-1-1-11-11ii−i−i−iii−ii−i−ii−ii11-1-1-1-111ii−i−i−i−iii-11−ii
χ121111-1-1-1-1i−i11-1-1-1-1111-11-11-11-1iii−i−i−i−ii-1-11111-1-1-1-111i−i1111-1-1-1-1-111-1−i−iiii−i−ii−ii−iii−i-1-111-1-111ii−i−i−i−iii1-1i−i
χ131111-1-1-1-1−ii11-1-111-1-11-11-11-11-1−i−i−iiii−ii1111-1-1-1-111-1-1−ii1111-1-1-1-11-11-1−i−iii−ii−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii1-1−ii
χ141111-1-1-1-1−ii11-1-111-1-11-11-11-11-1−i−i−iiii−ii-1-1-1-11111-1-111−ii1111-1-1-1-11-1-11ii−i−ii−ii−ii−i−iii−i-1-11111-1-1−i−iii−i−iii-11i−i
χ151111-1-1-1-1−ii11-1-1-1-1111-11-11-11-1−i−i−iiiii−i11-1-1-1-11111-1-1−ii1111-1-1-1-1-11-11−i−iiii−i−ii−iii−ii−i11-1-1-1-111−i−iiiii−i−i-11i−i
χ161111-1-1-1-1−ii11-1-1-1-1111-11-11-11-1−i−i−iiiii−i-1-11111-1-1-1-111−ii1111-1-1-1-1-111-1ii−i−i−iii−ii−ii−i−ii-1-111-1-111−i−iiiii−i−i1-1−ii
χ17222222222222222222222222222222222200000000000022-1-1-1-1-1-1-1-12200000000000022000000-1-1-1-1-1-1-1-1-1-1-1-10000
χ1822222222222222-2-2-2-222222222222222-2-200000000000022-1-1-1-1-1-1-1-1-2-2000000000000-2-20000001111-1-1-1-111110000
χ1922222222-2-22222222222222222-2-2-2-2-2-2-2-2000000000000-2-2-1-1-1-1-1-1-1-122000000000000-2-2000000-1-1-1-1111111110000
χ2022222222-2-22222-2-2-2-222222222-2-2-2-2-2-222000000000000-2-2-1-1-1-1-1-1-1-1-2-20000000000002200000011111111-1-1-1-10000
χ212222-2-2-2-22i−2i22-2-222-2-22-22-22-22-22i2i2i−2i−2i−2i2i−2i0000000000002i−2i-1-1-1-111112-20000000000002i−2i000000-1-111−i−iii−i−iii0000
χ222222-2-2-2-22i−2i22-2-2-2-2222-22-22-22-22i2i2i−2i−2i−2i−2i2i0000000000002i−2i-1-1-1-11111-22000000000000−2i2i00000011-1-1−i−iiiii−i−i0000
χ232222-2-2-2-2−2i2i22-2-222-2-22-22-22-22-2−2i−2i−2i2i2i2i−2i2i000000000000−2i2i-1-1-1-111112-2000000000000−2i2i000000-1-111ii−i−iii−i−i0000
χ242222-2-2-2-2−2i2i22-2-2-2-2222-22-22-22-2−2i−2i−2i2i2i2i2i−2i000000000000−2i2i-1-1-1-11111-220000000000002i−2i00000011-1-1ii−i−i−i−iii0000
χ252-2-2222-2-200-22-220000-222-2-2-222000000002-2002-2002-22-2002-2-2222-2-20000000000000000002-22-20000000000000000
χ262-2-2222-2-200-22-220000-222-2-2-22200000000-2200-2200-22-22002-2-2222-2-2000000000000000000-22-220000000000000000
χ272-2-22-2-22200-222-20000-2-222-222-2000000002-200-22002-2-22002-2-22-2-2220000000000000000002-2-220000000000000000
χ282-2-22-2-22200-222-20000-2-222-222-200000000-22002-200-222-2002-2-22-2-222000000000000000000-222-20000000000000000
χ29333333333333333333-1-1-1-1-1-1-1-13-1-13-1-133111111111111-1-100000000-1-111-1-1-1-1111111-1-111-1-1-1-1000000000000-1-1-1-1
χ30333333333333333333-1-1-1-1-1-1-1-13-1-13-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-11111-1-1-1-1-1-1-1-1-1-111110000000000001111
χ3133333333333333-3-3-3-3-1-1-1-1-1-1-1-13-1-13-1-1-3-311-1-111-1-11111-1-10000000011-1-1-1-1-1-1-1-1111111-1-1-1-1-1-10000000000001111
χ3233333333333333-3-3-3-3-1-1-1-1-1-1-1-13-1-13-1-1-3-3-1-111-1-111-1-1-1-1-1-1000000001111111111-1-1-1-111111111000000000000-1-1-1-1
χ3333333333-3-333333333-1-1-1-1-1-1-1-1-311-311-3-31111111111111100000000-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1000000000000-1-111
χ3433333333-3-333333333-1-1-1-1-1-1-1-1-311-311-3-3-1-1-1-1-1-1-1-1-1-1-1-11100000000-1-1-1-1-1-1-1-11111111111111100000000000011-1-1
χ3533333333-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-311-3113311-1-111-1-11111110000000011-1-1111111-1-1-1-1-1-111-1-1-1-100000000000011-1-1
χ3633333333-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-311-31133-1-111-1-111-1-1-1-111000000001111-1-1-1-1-1-11111-1-1-1-11111000000000000-1-111
χ373333-3-3-3-33i−3i33-3-333-3-3-11-11-11-113i−i−i−3iii3i−3i1111-1-1-1-111-1-1−ii00000000-111-1−i−iiii−ii−ii−i−iii−i-1-111000000000000-11−ii
χ383333-3-3-3-33i−3i33-3-333-3-3-11-11-11-113i−i−i−3iii3i−3i-1-1-1-11111-1-111−ii00000000-11-11ii−i−i−ii−ii−ii−ii−ii11-1-10000000000001-1i−i
χ393333-3-3-3-33i−3i33-3-3-3-333-11-11-11-113i−i−i−3iii−3i3i11-1-1-1-11111-1-1−ii000000001-1-11−i−iii−iii−ii−ii−i−ii-1-1110000000000001-1i−i
χ403333-3-3-3-33i−3i33-3-3-3-333-11-11-11-113i−i−i−3iii−3i3i-1-11111-1-1-1-111−ii000000001-11-1ii−i−ii−i−ii−iii−ii−i11-1-1000000000000-11−ii
χ413333-3-3-3-3−3i3i33-3-333-3-3-11-11-11-11−3iii3i−i−i−3i3i1111-1-1-1-111-1-1i−i00000000-111-1ii−i−i−ii−ii−iii−i−ii-1-111000000000000-11i−i
χ423333-3-3-3-3−3i3i33-3-333-3-3-11-11-11-11−3iii3i−i−i−3i3i-1-1-1-11111-1-111i−i00000000-11-11−i−iiii−ii−ii−ii−ii−i11-1-10000000000001-1−ii
χ433333-3-3-3-3−3i3i33-3-3-3-333-11-11-11-11−3iii3i−i−i3i−3i11-1-1-1-11111-1-1i−i000000001-1-11ii−i−ii−i−ii−ii−iii−i-1-1110000000000001-1−ii
χ443333-3-3-3-3−3i3i33-3-3-3-333-11-11-11-11−3iii3i−i−i3i−3i-1-11111-1-1-1-111i−i000000001-11-1−i−iii−iii−ii−i−ii−ii11-1-1000000000000-11i−i
χ454-4-4444-4-400-44-440000-444-4-4-4440000000000000000000000-222-2-2-22200000000000000000000000000000000000000
χ464-4-44-4-44400-444-40000-4-444-444-40000000000000000000000-222-222-2-200000000000000000000000000000000000000
χ476666666666-2-2-2-200002-22-2-22-22-2-2-2-2-2-200002200220000220000000000-2-2000022000000-2-200000000000000000000
χ486666666666-2-2-2-200002-22-2-22-22-2-2-2-2-2-20000-2-200-2-20000220000000000220000-2-20000002200000000000000000000
χ496666666666-2-2-2-20000-22-222-22-2-222-2220022002200-2-2-2-2-2-200000000000000000022-2-2000000000000000000000000
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χ556666-6-6-6-66i−6i-2-22200002222-2-2-2-2−2i−2i−2i2i2i2i00002200-2-200002i−2i0000000000-2200002i−2i000000−2i2i00000000000000000000
χ566666-6-6-6-66i−6i-2-22200002222-2-2-2-2−2i−2i−2i2i2i2i0000-2-2002200002i−2i00000000002-20000−2i2i0000002i−2i00000000000000000000
χ576666-6-6-6-66i−6i-2-2220000-2-2-2-22222−2i2i2i2i−2i−2i002200-2-200-2-222−2i2i0000000000000000002i−2i−2i2i000000000000000000000000
χ586666-6-6-6-66i−6i-2-2220000-2-2-2-22222−2i2i2i2i−2i−2i00-2-200220022-2-2−2i2i000000000000000000−2i2i2i−2i000000000000000000000000
χ596666-6-6-6-6−6i6i-2-22200002222-2-2-2-22i2i2i−2i−2i−2i00002200-2-20000−2i2i0000000000-220000−2i2i0000002i−2i00000000000000000000
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χ616666-6-6-6-6−6i6i-2-2220000-2-2-2-222222i−2i−2i−2i2i2i002200-2-200-2-2222i−2i000000000000000000−2i2i2i−2i000000000000000000000000
χ626666-6-6-6-6−6i6i-2-2220000-2-2-2-222222i−2i−2i−2i2i2i00-2-200220022-2-22i−2i0000000000000000002i−2i−2i2i000000000000000000000000
χ636-6-6666-6-6002-22-2000022-2-2-222-204i−4i04i−4i002-2002-200-22-22000000000000002i−2i2i−2i000000000000000000000000000000
χ646-6-6666-6-6002-22-2000022-2-2-222-204i−4i04i−4i00-2200-22002-22-200000000000000−2i2i−2i2i000000000000000000000000000000
χ656-6-6666-6-6002-22-2000022-2-2-222-20−4i4i0−4i4i002-2002-200-22-2200000000000000−2i2i−2i2i000000000000000000000000000000
χ666-6-6666-6-6002-22-2000022-2-2-222-20−4i4i0−4i4i00-2200-22002-22-2000000000000002i−2i2i−2i000000000000000000000000000000
χ676-6-6666-6-600-66-6600002-2-2222-2-2000000002-2002-2002-22-20000000000000000000000000000-22-220000000000000000
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χ746-6-66-6-66600-666-6000022-2-22-2-2200000000-22002-200-222-200000000000000000000000000002-2-220000000000000000
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χ818-88-88i−8i−8i8i0000004-44i−4i000000000000000000000000000000-11-11−iii−i0000000000000000000000-11−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ828-88-88i−8i−8i8i000000-44−4i4i0000000000000000000000000000002-22-22i−2i−2i2i0000000000000000000000-22−2i2i000000000000
χ838-88-88i−8i−8i8i000000-44−4i4i000000000000000000000000000000-11-11−iii−i00000000000000000000001-1i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ848-88-88i−8i−8i8i000000-44−4i4i000000000000000000000000000000-11-11−iii−i00000000000000000000001-1i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ858-88-8−8i8i8i−8i0000004-4−4i4i0000000000000000000000000000002-22-2−2i2i2i−2i00000000000000000000002-2−2i2i000000000000
χ868-88-8−8i8i8i−8i0000004-4−4i4i000000000000000000000000000000-11-11i−i−ii0000000000000000000000-11i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
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χ908-88-8−8i8i8i−8i000000-444i−4i000000000000000000000000000000-11-11i−i−ii00000000000000000000001-1−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ9112-12-12121212-12-12004-44-40000-4-4444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ9212-12-1212-12-121212004-4-440000-444-444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ931616-16-1616i−16i16i−16i0000000000000000000000000000000000000000-2-222−2i2i−2i2i00000000000000000000000000000000000000
χ941616-16-16−16i16i−16i16i0000000000000000000000000000000000000000-2-2222i−2i2i−2i00000000000000000000000000000000000000

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