Finite Group Databasebeta

← Group #11786614

Character table — Group #11786614

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order122222334444666666666636666666661212121212121212441212121212121212121212121212121212121212444444444444121212121212121288121212121212121224242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1
χ911-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-1i−ii−iii−i−iiiii−i−i−i−i1-1i−ii−i11-1-111-1-1i−ii−i1-1
χ1011-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i11-1-1−ii−iiii−i−iiiii−i−i−i−i-11−ii−ii11-1-1-1-111−ii−ii-11
χ1111-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i-1-111i−ii−i−i−iii−i−i−i−iiiii1-1i−ii−i-1-11111-1-1−ii−ii-11
χ1211-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11i−iii−i−iii−i−i11-1-1iiii−i−i−i−i-1-111−ii−ii−i−iii−i−i−i−iiiii-11−ii−ii-1-111-1-111i−ii−i1-1
χ1311-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-1i−ii−i−i−iii−i−i−i−iiiii-11i−ii−i11-1-1-1-111i−ii−i-11
χ1411-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii11-1-1−ii−ii−i−iii−i−i−i−iiiii1-1−ii−ii11-1-111-1-1−ii−ii1-1
χ1511-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii-1-111i−ii−iii−i−iiiii−i−i−i−i-11i−ii−i-1-111-1-111−ii−ii1-1
χ1611-1-11-111-1-11111-11-1-1-1-1-1111-111-1-1-11-11-1-111-1-11−ii−i−iii−i−iii11-1-1−i−i−i−iiiii-1-111−ii−iiii−i−iiiii−i−i−i−i1-1−ii−ii-1-11111-1-1i−ii−i-11
χ1722222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-20000000000-2-2-2-2000000002-22-200000000000000000000002-22-20000000000
χ1822222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-20000000000-2-2-2-200000000-22-220000000000000000000000-22-220000000000
χ192222222-12222222-1222-1-12-1-1-1-1-1-1-1-1-1-1-1-1-12222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222200000000000022-1-1-1-10000-1-1-1-1000000
χ202222222-12222222-1222-1-12-1-1-1-1-1-1-1-1-1-1-1-1-12222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000000000-2-2111100001111000000
χ212222222-12222222-1222-1-12-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-2-21111-1-1-1-11111111100002222000000000000-2-2-1-1-1-100001111000000
χ222222222-12222222-1222-1-12-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-2-21111-1-1-1-1111111110000-2-2-2-20000000000002211110000-1-1-1-1000000
χ23222222-122222-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200002222-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ24222222-122222-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-21111111100000011110000000000
χ25222222-122222-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1222-1-1-1-12-2-21111-2-2-2-2-1-1-1-11111111122220000-2-2-2-211111111000000-1-1-1-10000000000
χ26222222-122222-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1222-1-1-1-12-2-21111-2-2-2-2-1-1-1-111111111-2-2-2-200002222-1-1-1-1-1-1-1-100000011110000000000
χ27222222-12-2-2-2-2-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1-2-2-21111-200−i3i3−i3i300001111−i3−i3i3i3−i3−i3i3i32-22-200000000−i3−i3i3i3−i3−i3i3i3000000-11-110000000000
χ28222222-12-2-2-2-2-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1-2-2-21111-200−i3i3−i3i300001111−i3−i3i3i3−i3−i3i3i3-22-2200000000i3i3−i3−i3i3i3−i3−i30000001-11-10000000000
χ29222222-12-2-2-2-2-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1-2-2-21111-200i3−i3i3−i300001111i3i3−i3−i3i3i3−i3−i32-22-200000000i3i3−i3−i3i3i3−i3−i3000000-11-110000000000
χ30222222-12-2-2-2-2-1-1-12-1-1-122-1-122-1-1-1-1-1-1-1-2-2-21111-200i3−i3i3−i300001111i3i3−i3−i3i3i3−i3−i3-22-2200000000−i3−i3i3i3−i3−i3i3i30000001-11-10000000000
χ312222-2-2222-22-2-2-2222-2-22222-2-2-2-22-2-222-22-22-22-2200000000002-22-200000000000022-2-20000000000000022-2-200000000000000
χ322222-2-2222-22-2-2-2222-2-22222-2-2-2-22-2-222-22-22-22-2200000000002-22-2000000000000-2-22200000000000000-2-22200000000000000
χ332222-2-222-22-22-2-2222-2-22222-2-2-2-22-2-2222-22-22-22-20000000000-22-2200000000000000000000000000000000000000000022-2-200
χ342222-2-222-22-22-2-2222-2-22222-2-2-2-22-2-2222-22-22-22-20000000000-22-22000000000000000000000000000000000000000000-2-22200
χ352222-2-22-12-22-2-2-22-12-2-2-1-12-11111-111-1-11-112-22-2-1000000−i3i3−i3i3-11-11−i3i3−i3i3−i3i3−i3i3000022-2-200000000000000-1-1110000−i3i3−i3i3000000
χ362222-2-22-12-22-2-2-22-12-2-2-1-12-11111-111-1-11-112-22-2-1000000−i3i3−i3i3-11-11−i3i3−i3i3−i3i3−i3i30000-2-2220000000000000011-1-10000i3−i3i3−i3000000
χ372222-2-22-12-22-2-2-22-12-2-2-1-12-11111-111-1-11-112-22-2-1000000i3−i3i3−i3-11-11i3−i3i3−i3i3−i3i3−i3000022-2-200000000000000-1-1110000i3−i3i3−i3000000
χ382222-2-22-12-22-2-2-22-12-2-2-1-12-11111-111-1-11-112-22-2-1000000i3−i3i3−i3-11-11i3−i3i3−i3i3−i3i3−i30000-2-2220000000000000011-1-10000−i3i3−i3i3000000
χ3922-2-22-22222-2-222-22-2-2-2-2-2222-222-2-2-22-2-222-2-222-20000000000-2-222000000002-2-2200000000000000000000002-2-220000000000
χ4022-2-22-22222-2-222-22-2-2-2-2-2222-222-2-2-22-2-222-2-222-20000000000-2-22200000000-222-20000000000000000000000-222-20000000000
χ4122-2-22-22-1-2-22222-2-1-2-2-2112-1-11-1-1111-11-11122-2-2-12i−2i2i2i−2i−2i−i−iii-1-111−i−i−i−iiiii00002i−2i2i−2i0000000000002-2−ii−ii0000-1-111000000
χ4222-2-22-22-1-2-22222-2-1-2-2-2112-1-11-1-1111-11-11122-2-2-12i−2i2i2i−2i−2i−i−iii-1-111−i−i−i−iiiii0000−2i2i−2i2i000000000000-22i−ii−i000011-1-1000000
χ4322-2-22-22-1-2-22222-2-1-2-2-2112-1-11-1-1111-11-11122-2-2-1−2i2i−2i−2i2i2iii−i−i-1-111iiii−i−i−i−i00002i−2i2i−2i000000000000-22−ii−ii000011-1-1000000
χ4422-2-22-22-1-2-22222-2-1-2-2-2112-1-11-1-1111-11-11122-2-2-1−2i2i−2i−2i2i2iii−i−i-1-111iiii−i−i−i−i0000−2i2i−2i2i0000000000002-2i−ii−i0000-1-111000000
χ4522-2-22-2-1222-2-2-1-112111-2-2-1-12-2-1-1111-11-22211-1-1-2003−3−33000011-1-133−3−3−3−3332-2-220000000033−3−3−3−333000000-111-10000000000
χ4622-2-22-2-1222-2-2-1-112111-2-2-1-12-2-1-1111-11-22211-1-1-2003−3−33000011-1-133−3−3−3−333-222-200000000−3−33333−3−30000001-1-110000000000
χ4722-2-22-2-1222-2-2-1-112111-2-2-1-12-2-1-1111-11-22211-1-1-200−333−3000011-1-1−3−33333−3−32-2-2200000000−3−33333−3−3000000-111-10000000000
χ4822-2-22-2-1222-2-2-1-112111-2-2-1-12-2-1-1111-11-22211-1-1-200−333−3000011-1-1−3−33333−3−3-222-20000000033−3−3−3−3330000001-1-110000000000
χ4922-2-22-2-12-2-222-1-112111-2-2-1-12-2-1-1111-112-2-2-1-11122i−2i−i−iii2i2i−2i−2i-1-111−i−i−i−iiiii22-2-200002i2i−2i−2i−i−i−i−iiiii000000-1-1110000000000
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χ5222-2-22-2-12-2-222-1-112111-2-2-1-12-2-1-1111-112-2-2-1-1112−2i2iii−i−i−2i−2i2i2i-1-111iiii−i−i−i−i-2-22200002i2i−2i−2i−i−i−i−iiiii00000011-1-10000000000
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χ5422-2-2-22222-2-22-2-2-22-222-2-222-22-2-2-2222-222-2-222-2-20000000000-222-2000000000000000000000000000000000000000000−2i2i2i−2i00
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χ5622-2-2-2222-222-2-2-2-22-222-2-222-22-2-2-2222-2-2-222-2-22200000000002-2-22000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000
χ5722-2-2-222-1-222-2-2-2-2-1-222112-11-1111-1-1-1111-12-2-22-10000003−3−33-111-13−33−3−33−3300002i−2i−2i2i00000000000000−iii−i0000−i3i3i3−i3000000
χ5822-2-2-222-1-222-2-2-2-2-1-222112-11-1111-1-1-1111-12-2-22-10000003−3−33-111-13−33−3−33−330000−2i2i2i−2i00000000000000i−i−ii0000i3−i3−i3i3000000
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χ914-4-440044000000-4-4400-44-440000-400-44000000000000000000000000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000
χ924-4-440044000000-4-4400-44-440000-400-4400000000000000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ934-4-4400-240000−2i32i32-4-22i3−2i3-442-200−2i32i322i3−2i32-2000000000000000000000000000000000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ944-4-4400-240000−2i32i32-4-22i3−2i3-442-200−2i32i322i3−2i32-200000000000000000000000000000000000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ954-4-4400-2400002i3−2i32-4-2−2i32i3-442-2002i3−2i32−2i32i32-2000000000000000000000000000000000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ964-4-4400-2400002i3−2i32-4-2−2i32i3-442-2002i3−2i32−2i32i32-200000000000000000000000000000000000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ978-88-8008-400000084-800-44-8-40000-400440000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-800-4-40000−4i34i3-444−4i34i3-4442002i3−2i322i3−2i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ998-88-800-4-400004i3−4i3-4444i3−4i3-444200−2i32i32−2i32i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-4000000-848004-4-8-400004004-40000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-40000−4i34i344-44i3−4i34-442002i3−2i3-2−2i32i3-220000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-400004i3−4i344-4−4i34i34-44200−2i32i3-22i3−2i3-220000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.