Finite Group Databasebeta

← Group #11780116

Character table — Group #11780116

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order1222334444666666121212123444666121212121212121212121212121212122666666661212121212121212121212226666888824242424242424244448812121212121224242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-11111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ7111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1
χ92222222-2-22222222-2-2-2-2222-22222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000
χ102222222-2-22222222-2-2-2-22-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-2-222-2-2-2-2-2-2000000000000000000000000000000000000
χ11222222-222-22222222222200-2222-2-2-2-22200002222-2-2000000000-200-2-2-2-20000222222000000000000-20000-2-200000000000
χ12222222-222-22222222222200-2222-2-2-2-22200002222-2-2000000000-200-2-2-2-20000-2-2-2-2-2-2000000000000200002200000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-222000000000200-2-222000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-222000000000200-2-22200000000000000000000000-220000-2-2220000000
χ1522222-1222222-12-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000022200-1-1-1-1-1-10000000
χ1622222-1222222-12-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111000000000000-2-2-2001111110000000
χ1722222-1222222-12-1-12222-1-2-22-1-1-122-1-1-1-11111-1-1-1-122-2-2-2111111-1-2-2-1-1-1-1111122-1-1-1-10000000000002-2-200-1-111110000000
χ1822222-1222222-12-1-12222-1-2-22-1-1-122-1-1-1-11111-1-1-1-122-2-2-2111111-1-2-2-1-1-1-11111-2-21111000000000000-2220011-1-1-1-10000000
χ1922222-12-2-2222-12-1-1-2-2-2-2-122-2-1-1-122-1-111-1-1-1-11111-2-2-2-2-2111111122-1-111-1-1-1-100−i3−i3i3i300000000000000000−i3i3−i3i3−i3i30000000
χ2022222-12-2-2222-12-1-1-2-2-2-2-122-2-1-1-122-1-111-1-1-1-11111-2-2-2-2-2111111122-1-111-1-1-1-100i3i3−i3−i300000000000000000i3−i3i3−i3i3−i30000000
χ2122222-12-2-2222-12-1-1-2-2-2-2-1-2-2-2-1-1-122-1-11111111111-2-2222-1-1-1-1-1-11-2-2-1-111111100−i3−i3i3i300000000000000000−i3i3i3−i3i3−i30000000
χ2222222-12-2-2222-12-1-1-2-2-2-2-1-2-2-2-1-1-122-1-11111111111-2-2222-1-1-1-1-1-11-2-2-1-111111100i3i3−i3−i300000000000000000i3−i3−i3i3−i3i30000000
χ2322222-1-222-222-12-1-12222-100-2-1-1-1-2-211-1-1−i3−i3i3i3-1-1-1-1-2-2000−i3i3−i3−i3i3i31001111−i3−i3i3i322-1-1-1-1000000000000-2000011−i3i3i3−i30000000
χ2422222-1-222-222-12-1-12222-100-2-1-1-1-2-211-1-1−i3−i3i3i3-1-1-1-1-2-2000−i3i3−i3−i3i3i31001111−i3−i3i3i3-2-2111100000000000020000-1-1i3−i3−i3i30000000
χ2522222-1-222-222-12-1-12222-100-2-1-1-1-2-211-1-1i3i3−i3−i3-1-1-1-1-2-2000i3−i3i3i3−i3−i31001111i3i3−i3−i322-1-1-1-1000000000000-2000011i3−i3−i3i30000000
χ2622222-1-222-222-12-1-12222-100-2-1-1-1-2-211-1-1i3i3−i3−i3-1-1-1-1-2-2000i3−i3i3i3−i3−i31001111i3i3−i3−i3-2-2111100000000000020000-1-1−i3i3i3−i30000000
χ2722222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111−i3−i3i3i3111122000i3−i3i3i3−i3−i3-10011-1-1−i3−i3i3i300−i3−i3i3i300000000000002-200i3−i3-1-1110000000
χ2822222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111−i3−i3i3i3111122000i3−i3i3i3−i3−i3-10011-1-1−i3−i3i3i300i3i3−i3−i30000000000000-2200−i3i311-1-10000000
χ2922222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111i3i3−i3−i3111122000−i3i3−i3−i3i3i3-10011-1-1i3i3−i3−i300−i3−i3i3i30000000000000-2200i3−i311-1-10000000
χ3022222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111i3i3−i3−i3111122000−i3i3−i3−i3i3i3-10011-1-1i3i3−i3−i300i3i3−i3−i300000000000002-200−i3i3-1-1110000000
χ312222-122222-1-12-122-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-1-1-1-1-10000002222-1-1-1-1-1-1-1-100022000000-1-1-1-1000
χ322222-122222-1-12-122-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-1-1-1-1-1000000-2-2-2-211111111000-2-20000001111000
χ332222-122222-1-12-122-1-1-1-1-1-2-22-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-211-2-21111211-1-1-1-111110000002222-1-1-1-1-1-1-1-1000-2-20000001111000
χ342222-122222-1-12-122-1-1-1-1-1-2-22-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-211-2-21111211-1-1-1-11111000000-2-2-2-21111111100022000000-1-1-1-1000
χ352222-122-2-22-1-12-1221111-122-2-1-1-1-1-122-2-22222111111-211-2-21111-2-1-1-1-111-1-1-1-100000000003333−3−3−3−30000000000033−3−3000
χ362222-122-2-22-1-12-1221111-122-2-1-1-1-1-122-2-22222111111-211-2-21111-2-1-1-1-111-1-1-1-10000000000−3−3−3−3333300000000000−3−333000
χ372222-122-2-22-1-12-1221111-1-2-2-2-1-1-1-1-122-2-2-2-2-2-21111112-1-122-1-1-1-1-211-1-111111100000000003333−3−3−3−300000000000−3−333000
χ382222-122-2-22-1-12-1221111-1-2-2-2-1-1-1-1-122-2-2-2-2-2-21111112-1-122-1-1-1-1-211-1-11111110000000000−3−3−3−333330000000000033−3−3000
χ392-22-222-20022-2-2-22-2000022i−2i02-2-22-22-2002i−2i2i−2i00000000000000002i−2i2-2002i−2i2i−2i00000022−2−222−2−222−2−2000−i2i2000000−i2i2−i2i2000
χ402-22-222-20022-2-2-22-2000022i−2i02-2-22-22-2002i−2i2i−2i00000000000000002i−2i2-2002i−2i2i−2i000000−2−222−2−222−2−222000i2−i2000000i2−i2i2−i2000
χ412-22-222-20022-2-2-22-200002−2i2i02-2-22-22-200−2i2i−2i2i0000000000000000−2i2i2-200−2i2i−2i2i00000022−2−222−2−222−2−2000i2−i2000000i2−i2i2−i2000
χ422-22-222-20022-2-2-22-200002−2i2i02-2-22-22-200−2i2i−2i2i0000000000000000−2i2i2-200−2i2i−2i2i000000−2−222−2−222−2−222000−i2i2000000−i2i2−i2i2000
χ432-22-2-12-2002-11-212-23−33−3-12i−2i0-111-112-2002i−2i2i−2i33−3−33−30−i3i300−i3i3−i3i30−ii-113−3−ii−ii00000022−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000−i2i2000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ442-22-2-12-2002-11-212-23−33−3-12i−2i0-111-112-2002i−2i2i−2i33−3−33−30−i3i300−i3i3−i3i30−ii-113−3−ii−ii000000−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000i2−i2000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ452-22-2-12-2002-11-212-23−33−3-1−2i2i0-111-112-200−2i2i−2i2i33−3−33−30i3−i300i3−i3i3−i30i−i-113−3i−ii−i00000022−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000i2−i2000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ462-22-2-12-2002-11-212-23−33−3-1−2i2i0-111-112-200−2i2i−2i2i33−3−33−30i3−i300i3−i3i3−i30i−i-113−3i−ii−i000000−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000−i2i2000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ472-22-2-12-2002-11-212-2−33−33-12i−2i0-111-112-2002i−2i2i−2i−3−333−330i3−i300i3−i3i3−i30−ii-11−33−ii−ii00000022−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000−i2i2000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ482-22-2-12-2002-11-212-2−33−33-12i−2i0-111-112-2002i−2i2i−2i−3−333−330i3−i300i3−i3i3−i30−ii-11−33−ii−ii000000−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000i2−i2000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ492-22-2-12-2002-11-212-2−33−33-1−2i2i0-111-112-200−2i2i−2i2i−3−333−330−i3i300−i3i3−i3i30i−i-11−33i−ii−i00000022−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000i2−i2000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ502-22-2-12-2002-11-212-2−33−33-1−2i2i0-111-112-200−2i2i−2i2i−3−333−330−i3i300−i3i3−i3i30i−i-11−33i−ii−i000000−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000−i2i2000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ512-2-22220-220-2-2-22-22-2-2222000-2-2200002-200002-22-200000000000000000000002-22-22-22−22−22−22−22−22−20000000000000002−20
χ522-2-22220-220-2-2-22-22-2-2222000-2-2200002-200002-22-200000000000000000000002-22-22-2−22−22−22−22−22−22000000000000000−220
χ532-2-22220-220-2-2-22-22-2-2222000-2-2200002-200002-22-20000000000000000000000-22-22-222−22−22−22−22−22−2000000000000000−220
χ542-2-22220-220-2-2-22-22-2-2222000-2-2200002-200002-22-20000000000000000000000-22-22-22−22−22−22−22−22−220000000000000002−20
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χ604444-2-24-4-44-2-2-2-2-2-222221-4-4-4111-2-2-2-2222222-1-1-1-1224-2-2-2-2111122211-1-1-1-1-1-1000000000000000000000000000000000000
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χ634444-2-2-4-4-4-4-2-2-2-2-2-222221004111222222−2i3−2i32i32i3-1-1-1-1-2-20002i3−2i3−i3−i3i3i3-200-1-111i3i3−i3−i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-2222210041112222222i32i3−2i3−2i3-1-1-1-1-2-2000−2i32i3i3i3−i3−i3-200-1-111−i3−i3i3i3000000000000000000000000000000000000
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χ844-44-4-2-2-4004-2222-22−2323−232314i−4i01-1-1-22-2200−2i2i−2i2i33−3−3−232302i3−2i300−i3i3−i3i30−2i2i1-13−3i−ii−i000000000000000000000000000000000000
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χ924-4-44-2404-4022-4-2-44-2-222-200022-20000-4400002-22-200000000000000000000000000000000−66−666−66−6000000000000000000
χ934-4-44-240-44022-4-2-4422-2-2-200022-200004-40000-22-22000000000000000000000000000022−2222−22−22−22−22−22000000000000000000
χ944-4-44-240-44022-4-2-4422-2-2-200022-200004-40000-22-220000000000000000000000000000−2222−22222−22−22−22−2000000000000000000
χ9588-8-88-40000-88-4-8440000-40004-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-400004-4-444443−43−43432000-22-2000000000023−23−23230000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-400004-4-4444−434343−432000-22-20000000000−232323−230000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-408-80444-44-4-4-4442000-2-2200004-40000-22-220000000000000000000000000000000000000000000000000000000000
χ998-8-88-4-40-880444-44-444-4-42000-2-220000-4400002-22-20000000000000000000000000000000000000000000000000000000000

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