Finite Group Databasebeta

← Group #11786735

Character table — Group #11786735

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order1222223344446666666666366666666612121212121212124412121212121212121212121212121212121212122244444444441212121212121212668812121212121224242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1
χ911-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-11-1ii−i−i11-1-11111-1-1-1-11-1i−i1-1ii−i−iii−i−ii−ii−i1-1
χ1011-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-11-1−i−iii-1-111-1-1-1-111111-1i−i1-1−i−iiiii−i−i−ii−ii-11
χ1111-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i-11-11ii−i−i11-1-11111-1-1-1-1-11−ii-11ii−i−i−i−iii−ii−ii-11
χ1211-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i-11-11−i−iii-1-111-1-1-1-11111-11−ii-11−i−iii−i−iiii−ii−i1-1
χ1311-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-11-1ii−i−i-1-111-1-1-1-111111-1−ii1-1ii−i−i−i−iiii−ii−i-11
χ1411-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-11-1−i−iii11-1-11111-1-1-1-11-1−ii1-1−i−iii−i−iii−ii−ii1-1
χ1511-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii-11-11ii−i−i-1-111-1-1-1-11111-11i−i-11ii−i−iii−i−i−ii−ii1-1
χ1611-1-1-11111-1-11-1-1-11-1-1111-111-111-1-1-11-111-1-111-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii-11-11−i−iii11-1-11111-1-1-1-1-11i−i-11−i−iiiii−i−ii−ii−i-11
χ1722222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-20000000000-2-2-2-20000000000002-22-20000000000000000002-22-20000000000
χ1822222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-20000000000-2-2-2-2000000000000-22-22000000000000000000-22-220000000000
χ192222222-1222222-122-122-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-122-1-10000-1-1-1-1000000
χ202222222-1222222-122-122-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000011-2-21100001111000000
χ212222222-1222222-122-122-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211-2-211-1-1-1-11111111122220000000000000000-1-1-2-2-1-100001111000000
χ222222222-1222222-122-122-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211-2-211-1-1-1-111111111-2-2-2-200000000000000001122110000-1-1-1-1000000
χ23222222-122222-1-12-1-12-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1222222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ24222222-122222-1-12-1-12-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1222222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-21111111100000011110000000000
χ25222222-122222-1-12-1-12-1-12-1-122-1-1-1-1-1-1-1-1-1-1-12222-2-211-2-211-2-2-1-1-1-11111111100002222-2-2-2-211111111000000-1-1-1-10000000000
χ26222222-122222-1-12-1-12-1-12-1-122-1-1-1-1-1-1-1-1-1-1-12222-2-211-2-211-2-2-1-1-1-1111111110000-2-2-2-22222-1-1-1-1-1-1-1-100000011110000000000
χ27222222-12-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-1-1-1-11111-2-2-2-200−i3i300−i3i3001111−i3−i3i3i3−i3−i3i3i300002-22-20000−i3−i3i3i3−i3−i3i3i3000000-11-110000000000
χ28222222-12-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-1-1-1-11111-2-2-2-200−i3i300−i3i3001111−i3−i3i3i3−i3−i3i3i30000-22-220000i3i3−i3−i3i3i3−i3−i30000001-11-10000000000
χ29222222-12-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-1-1-1-11111-2-2-2-200i3−i300i3−i3001111i3i3−i3−i3i3i3−i3−i300002-22-20000i3i3−i3−i3i3i3−i3−i3000000-11-110000000000
χ30222222-12-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-1-1-1-11111-2-2-2-200i3−i300i3−i3001111i3i3−i3−i3i3i3−i3−i30000-22-220000−i3−i3i3i3−i3−i3i3i30000001-11-10000000000
χ312222-2-2222-22-2-2-22222-2-2222-2-2-2-22-2-2222-22-22-2-2200000000002-22-20000000022-2-200000000000000002200-2-200000000000000
χ322222-2-2222-22-2-2-22222-2-2222-2-2-2-22-2-2222-22-22-2-2200000000002-22-200000000-2-2220000000000000000-2-2002200000000000000
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χ4122-2-22-222-2-22222-22-2-2-2-22-22-22-2-2-2222-2-222-2-22-220000000000-222-20000000000000000000000000000000000000000002i−2i−2i2i00
χ4222-2-22-222-2-22222-22-2-2-2-22-22-22-2-2-2222-2-222-2-22-220000000000-222-2000000000000000000000000000000000000000000−2i2i2i−2i00
χ4322-2-22-22-122-2-22212-21-2-2-1-2-11-1111-1-1-112-2-22-11-1100003−300−33-111-13−33−3−33−332-2-220000000000000000-11001-100003−3−33000000
χ4422-2-22-22-122-2-22212-21-2-2-1-2-11-1111-1-1-112-2-22-11-1100003−300−33-111-13−33−3−33−33-222-200000000000000001-100-110000−333−3000000
χ4522-2-22-22-122-2-22212-21-2-2-1-2-11-1111-1-1-112-2-22-11-110000−33003−3-111-1−33−333−33−32-2-220000000000000000-11001-10000−333−3000000
χ4622-2-22-22-122-2-22212-21-2-2-1-2-11-1111-1-1-112-2-22-11-110000−33003−3-111-1−33−333−33−3-222-200000000000000001-100-1100003−3−33000000
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χ5522-2-2-22-122-2-2211-2-11-2-1-121-12-2-1-1111-11-1-11122-2-2−2i2iii−2i−2i−i−i2i2i-1-111iiii−i−i−i−i00002i2i−2i−2i-2-2221111-1-1-1-1000000−i−iii0000000000
χ5622-2-2-22-122-2-2211-2-11-2-1-121-12-2-1-1111-11-1-11122-2-2−2i2iii−2i−2i−i−i2i2i-1-111iiii−i−i−i−i0000−2i−2i2i2i22-2-2-1-1-1-11111000000ii−i−i0000000000
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χ914-4-4400440000004-4-4-400-4440000400-4-4000000000000000000000000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000
χ924-4-4400440000004-4-4-400-4440000400-4-400000000000000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ934-4-4400-240000−2i32i3422-42i3−2i3-4-2-2002i3−2i3-2−2i32i322000000000000000000000000000000000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000
χ944-4-4400-240000−2i32i3422-42i3−2i3-4-2-2002i3−2i3-2−2i32i32200000000000000000000000000000000000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000
χ954-4-4400-2400002i3−2i3422-4−2i32i3-4-2-200−2i32i3-22i3−2i322000000000000000000000000000000000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000
χ964-4-4400-2400002i3−2i3422-4−2i32i3-4-2-200−2i32i3-22i3−2i32200000000000000000000000000000000000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000
χ978-88-8008-40000004-88-4004-8-400004004-40000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-800-4-40000−4i34i344-4-4−4i34i3442002i3−2i3-22i3−2i3-220000000000000000000000000000000000000000000000000000000000000000000000
χ998-88-800-4-400004i3−4i344-4-44i3−4i344200−2i32i3-2−2i32i3-220000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-4000000-4-8-840048-40000-400440000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-40000−4i34i3-44444i3−4i34-4200−2i32i322i3−2i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-400004i3−4i3-4444−4i34i34-42002i3−2i32−2i32i3-2-20000000000000000000000000000000000000000000000000000000000000000000000

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