Finite Group Databasebeta

← Group #11780210

Character table — Group #11780210

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order122233444466666612121212223466666661212121212121212121212124666666121212121212121212121212124488881212121224242424242424244448812121212121224242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1
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
χ511111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1
χ611111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ711111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-11111-1-1-1-1-1-11
χ811111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1
χ92222222-2-22222222-2-2-2-2222-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2-2-2-2000000000000000000000000000000000000
χ102222222-2-22222222-2-2-2-2-2-22-2-2-2-2-22222222-2-2-2-2-2-2-2-22-2-2-2-2-2-222-22222-2-22222000000000000000000000000000000000000
χ11222222-222-22222222222002-20000222-2-2-2-2222222-2-2000000000-200-2-2-2-20000220000222200000000-20000-2-200000000000
χ12222222-222-22222222222002-20000222-2-2-2-2222222-2-2000000000-200-2-2-2-20000-2-20000-2-2-2-200000000200002200000000000
χ13222222-2-2-2-2222222-2-2-2-200220000222-2-2-2-2-2-2-2-2-2-222000000000200-2-222000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-200220000222-2-2-2-2-2-2-2-2-2-222000000000200-2-22200000000000000000000000-220000-2-2220000000
χ1522222-1222222-12-1-1222222-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1220000-1-1-1-10000000022200-1-1-1-1-1-10000000
χ1622222-1222222-12-1-1222222-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-20000111100000000-2-2-2001111110000000
χ1722222-1222222-12-1-12222-2-2-121111-1-1-122-1-1-1-1-1-1-1-122-2-2-21111-2-2-111-1-1-1-11111220000-1-1-1-1000000002-2-200-1-111110000000
χ1822222-1222222-12-1-12222-2-2-121111-1-1-122-1-1-1-1-1-1-1-122-2-2-21111-2-2-111-1-1-1-11111-2-20000111100000000-2220011-1-1-1-10000000
χ1922222-12-2-2222-12-1-1-2-2-2-222-1-2-1-1-1-1-1-1-122-1-1111111-2-2-222-1-1-1-1-2-2111-1-1111111000000−i3−i3i3i30000000000000−i3i3−i3i3−i3i30000000
χ2022222-12-2-2222-12-1-1-2-2-2-222-1-2-1-1-1-1-1-1-122-1-1111111-2-2-222-1-1-1-1-2-2111-1-1111111000000i3i3−i3−i30000000000000i3−i3i3−i3i3−i30000000
χ2122222-12-2-2222-12-1-1-2-2-2-2-2-2-1-21111-1-1-122-1-1111111-2-22-2-21111221-1-1-1-111-1-1-1-1000000−i3−i3i3i30000000000000−i3i3i3−i3i3−i30000000
χ2222222-12-2-2222-12-1-1-2-2-2-2-2-2-1-21111-1-1-122-1-1111111-2-22-2-21111221-1-1-1-111-1-1-1-1000000i3i3−i3−i30000000000000i3−i3−i3i3−i3i30000000
χ2322222-1-222-222-12-1-1222200-1-2−i3−i3i3i3-1-1-1-2-211-1-1-1-1-1-1-2-2000−i3−i3i3i3001−i3i31111−i3−i3i3i3220000-1-1-1-100000000-2000011−i3i3i3−i30000000
χ2422222-1-222-222-12-1-1222200-1-2−i3−i3i3i3-1-1-1-2-211-1-1-1-1-1-1-2-2000−i3−i3i3i3001−i3i31111−i3−i3i3i3-2-2000011110000000020000-1-1i3−i3−i3i30000000
χ2522222-1-222-222-12-1-1222200-1-2i3i3−i3−i3-1-1-1-2-211-1-1-1-1-1-1-2-2000i3i3−i3−i3001i3−i31111i3i3−i3−i3220000-1-1-1-100000000-2000011i3−i3−i3i30000000
χ2622222-1-222-222-12-1-1222200-1-2i3i3−i3−i3-1-1-1-2-211-1-1-1-1-1-1-2-2000i3i3−i3−i3001i3−i31111i3i3−i3−i3-2-2000011110000000020000-1-1−i3i3i3−i30000000
χ2722222-1-2-2-2-222-12-1-1-2-2-2-200-12−i3−i3i3i3-1-1-1-2-21111111122000−i3−i3i3i300-1i3−i311-1-1i3i3−i3−i3000000−i3−i3i3i30000000002-200i3−i3-1-1110000000
χ2822222-1-2-2-2-222-12-1-1-2-2-2-200-12−i3−i3i3i3-1-1-1-2-21111111122000−i3−i3i3i300-1i3−i311-1-1i3i3−i3−i3000000i3i3−i3−i3000000000-2200−i3i311-1-10000000
χ2922222-1-2-2-2-222-12-1-1-2-2-2-200-12i3i3−i3−i3-1-1-1-2-21111111122000i3i3−i3−i300-1−i3i311-1-1−i3−i3i3i3000000−i3−i3i3i3000000000-2200i3−i311-1-10000000
χ3022222-1-2-2-2-222-12-1-1-2-2-2-200-12i3i3−i3−i3-1-1-1-2-21111111122000i3i3−i3−i300-1−i3i311-1-1−i3−i3i3i3000000i3i3−i3−i30000000002-200−i3i3-1-1110000000
χ312222-122222-1-12-122-1-1-1-122-122222-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-100022000000-1-1-1-1000
χ322222-122222-1-12-122-1-1-1-122-122222-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-100-2-2-2-2000011111111000-2-20000001111000
χ332222-122222-1-12-122-1-1-1-1-2-2-12-2-2-2-2-1-1-1-1-12222-1-1-1-1-1-1-2111111112-2-2-1-1-1-111110022220000-1-1-1-1-1-1-1-1000-2-20000001111000
χ342222-122222-1-12-122-1-1-1-1-2-2-12-2-2-2-2-1-1-1-1-12222-1-1-1-1-1-1-2111111112-2-2-1-1-1-1111100-2-2-2-200001111111100022000000-1-1-1-1000
χ352222-122-2-22-1-12-122111122-1-22222-1-1-1-1-122-2-2111111-2-1-1-1-1-1-111-2-2-2-1-111111100000000003333−3−3−3−30000000000033−3−3000
χ362222-122-2-22-1-12-122111122-1-22222-1-1-1-1-122-2-2111111-2-1-1-1-1-1-111-2-2-2-1-11111110000000000−3−3−3−3333300000000000−3−333000
χ372222-122-2-22-1-12-1221111-2-2-1-2-2-2-2-2-1-1-1-1-122-2-21111112111111-1-1-222-1-111-1-1-1-100000000003333−3−3−3−300000000000−3−333000
χ382222-122-2-22-1-12-1221111-2-2-1-2-2-2-2-2-1-1-1-1-122-2-21111112111111-1-1-222-1-111-1-1-1-10000000000−3−3−3−333330000000000033−3−3000
χ3922-2-222200-22-22-2-2-200002-2202-22-22-2-22-22-20000000002-22-22-2000002-20000000022−2−2000022−2−222−2−20002−20000002−22−2000
χ4022-2-222200-22-22-2-2-200002-2202-22-22-2-22-22-20000000002-22-22-2000002-200000000−2−2220000−2−222−2−222000−22000000−22−22000
χ4122-2-222200-22-22-2-2-20000-2220-22-222-2-22-22-2000000000-22-22-22000002-20000000022−2−2000022−2−222−2−2000−22000000−22−22000
χ4222-2-222200-22-22-2-2-20000-2220-22-222-2-22-22-2000000000-22-22-22000002-200000000−2−2220000−2−222−2−2220002−20000002−22−2000
χ4322-2-2-12200-2-1121-2-23−33−32-2-102-22-2-111-112-20033−3−33−30-11-11-113−3000-113−33−33−30022−2−20000ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ230002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ4422-2-2-12200-2-1121-2-23−33−32-2-102-22-2-111-112-20033−3−33−30-11-11-113−3000-113−33−33−300−2−2220000−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ4522-2-2-12200-2-1121-2-23−33−3-22-10-22-22-111-112-20033−3−33−301-11-11-1−33000-113−3−33−330022−2−20000ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ4622-2-2-12200-2-1121-2-23−33−3-22-10-22-22-111-112-20033−3−33−301-11-11-1−33000-113−3−33−3300−2−2220000−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ230002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ4722-2-2-12200-2-1121-2-2−33−332-2-102-22-2-111-112-200−3−333−330-11-11-11−33000-11−33−33−330022−2−20000ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ70002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ4822-2-2-12200-2-1121-2-2−33−332-2-102-22-2-111-112-200−3−333−330-11-11-11−33000-11−33−33−3300−2−2220000−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ4922-2-2-12200-2-1121-2-2−33−33-22-10-22-22-111-112-200−3−333−3301-11-11-13−3000-11−333−33−30022−2−20000ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ5022-2-2-12200-2-1121-2-2−33−33-22-10-22-22-111-112-200−3−333−3301-11-11-13−3000-11−333−33−300−2−2220000−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ70002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ512-2-22220-220-2-2-22-22-2-22200200000-2-2200002-22-22-200000000000000000000002-22−22−22-22-22−22−22−22−20000000000000002−20
χ522-2-22220-220-2-2-22-22-2-22200200000-2-2200002-22-22-200000000000000000000002-2−22−222-22-2−22−22−22−22000000000000000−220
χ532-2-22220-220-2-2-22-22-2-22200200000-2-2200002-22-22-20000000000000000000000-222−22−2-22-222−22−22−22−2000000000000000−220
χ542-2-22220-220-2-2-22-22-2-22200200000-2-2200002-22-22-20000000000000000000000-22−22−22-22-22−22−22−22−220000000000000002−20
χ554444-24-444-4-2-24-244-2-2-2-200-2-40000-2-2-222-4-444-2-2-2-222000000000-40022220000000000000000000000000000000000000000
χ564444-24-4-4-4-4-2-24-244222200-240000-2-2-222-4-4-4-42222-2-200000000040022-2-20000000000000000000000000000000000000000
χ574444-2-24444-2-2-2-2-2-2-2-2-2-24414-2-2-2-2111-2-2-2-2-2-21111-2-24-2-21111-2-2-2-2-211111111000000000000000000000000000000000000
χ584444-2-24444-2-2-2-2-2-2-2-2-2-2-4-4142222111-2-2-2-2-2-21111-2-2-422-1-1-1-122-2221111-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-4-44-2-2-2-2-2-22222441-4-2-2-2-2111-2-2-2-222-1-1-1-122-4-2-211112222211-1-1-1-1-1-1000000000000000000000000000000000000
χ604444-2-24-4-44-2-2-2-2-2-22222-4-41-42222111-2-2-2-222-1-1-1-122422-1-1-1-1-2-22-2-211-1-11111000000000000000000000000000000000000
χ614444-2-2-444-4-2-2-2-2-2-2-2-2-2-2001-4−2i3−2i32i32i31112222-2-2111122000i3i3−i3−i3002−2i32i3-1-1-1-1i3i3−i3−i3000000000000000000000000000000000000
χ624444-2-2-444-4-2-2-2-2-2-2-2-2-2-2001-42i32i3−2i3−2i31112222-2-2111122000−i3−i3i3i30022i3−2i3-1-1-1-1−i3−i3i3i3000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-222220014−2i3−2i32i32i3111222222-1-1-1-1-2-2000i3i3−i3−i300-22i3−2i3-1-111−i3−i3i3i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-2222200142i32i3−2i3−2i3111222222-1-1-1-1-2-2000−i3−i3i3i300-2−2i32i3-1-111i3i3−i3−i3000000000000000000000000000000000000
χ6544-4-444-40044-44-4-4-40000004000004-4-4-44-4400000000000000000000-44000000000000000000000000000000000000000000
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χ6944-4-44-2-40044-4-2-422000000-202i3−2i3−2i32i3-222-442-2000000000002i3−2i3−2i32i3000002-2000000000000000000000000000000000000000000
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χ7544-4-4-2-2400-4-22-2222−2323−2323-44102-22-21-1-1-22-220033−3−3−232302-2-11-1123−230001-13−3−33−33000000000000000000000000000000000000
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χ7844-4-4-2-2-4004-22-2222−2323−23230010−2i32i32i3−2i31-1-12-22-20033−3−323−23000i3−i3−i3i300000-11−333i−3i−3i3i000000000000000000000000000000000000
χ7944-4-4-2-2-4004-22-2222−2323−232300102i3−2i3−2i32i31-1-12-22-20033−3−323−23000−i3i3i3−i300000-11−33−3i3i3i−3i000000000000000000000000000000000000
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χ844-44-4-2400002-2-424-4−232323−2300-2000002-2200000023−23−23230000000000000000000000002-2-220000−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000
χ854-44-4-2400002-2-424-4−232323−2300-2000002-2200000023−23−2323000000000000000000000000-222-200001−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000
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χ988-8-88-4-408-80444-44-4-4-44400200000-2-2200004-4-22-220000000000000000000000000000000000000000000000000000000000
χ998-8-88-4-40-880444-44-444-4-400200000-2-220000-442-22-20000000000000000000000000000000000000000000000000000000000

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