Finite Group Databasebeta

← Group #11781257

Character table — Group #11781257

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222222244444444444444444444444444444666666666666888888888888888881212121212121212121212121212121212122424242424244848487272144
order1222334444666666121212122234446666666121212121212121212121212121212128888242424242424242466666612121212121212121212128888882424242424242424242424248824242424266884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111-1-11-1-11-1-1-1-11111111111-1-1-1-111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ611111111111111111111-1-11-1-11-1-1-1-11111111111-1-1-1-111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ711111111111111111111-1-11-1-11-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11
χ811111111111111111111-1-11-1-11-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1
χ92222222-22-2222222222200200-20000222-2-2-2-2-22200002222-2222222222222000000-200-2-2-2-20000-2-20000-2-2-2-200000000000000000000
χ102222222-22-2222222222200200-20000222-2-2-2-2-22200002222-2-2-2-2-2-2-2-2-2-2-2-2-2000000-200-2-2-2-20000220000222200000000000000000000
χ11222222-22-22222222-2-2-2-2222-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22000000000000222222-2-2-222-2-2-2-2-2-2000000000000000000000000000000
χ12222222-22-22222222-2-2-2-2-2-2222-2-2-2-2-2222222-2-2-2-22222-2-2-2-22000000000000-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-20020020000222-2-2-222-2-20000-2-2-2-2-2000000000000000000200-2-2220000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i000000000000
χ14222222-2-2-2-2222222-2-2-2-20020020000222-2-2-222-2-20000-2-2-2-2-2000000000000000000200-2-222000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i000000000000
χ1522222-1222222-1-12-1222222-12222222-1-1-122-122-1-12222-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12-1-1000
χ1622222-1222222-1-12-1222222-12222222-1-1-122-122-1-12222-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-211000
χ1722222-1222222-1-12-12222-2-2-1-2-22-2-2-2-2-1-1-122-122-1-1-2-2-2-2-1-1-1-1-1000000000000111111-111-1-1-1-1111100000000000000000022-1-1-1-1-211000
χ1822222-1222222-1-12-12222-2-2-1-2-22-2-2-2-2-1-1-122-122-1-1-2-2-2-2-1-1-1-1-1000000000000111111-111-1-1-1-11111000000000000000000-2-211112-1-1000
χ1922222-1-22-2222-1-12-1-2-2-2-222-1-2-2-22222-1-1-122-1-2-211-2-2-2-21111-1000000000000-1-1-1-1-1-1111-1-111111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-1-22-2222-1-12-1-2-2-2-222-1-2-2-22222-1-1-122-1-2-211-2-2-2-21111-1000000000000-1-1-1-1-1-1111-1-111111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-1-22-2222-1-12-1-2-2-2-2-2-2-122-2-2-2-2-2-1-1-122-1-2-21122221111-10000000000001111111-1-1-1-111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-1-22-2222-1-12-1-2-2-2-2-2-2-122-2-2-2-2-2-1-1-122-1-2-21122221111-10000000000001111111-1-1-1-111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-1-122-12-1-1-1-122-1222-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ242222-122222-1-122-12-1-1-1-122-1222-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-12-2-2-2-21111111122-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111000000000000
χ252222-122222-1-122-12-1-1-1-1-2-2-1-2-221111-1-1-1-1-12-1-1221111-1-1-1-122222-1-1-1-1-1-1-1-1-2-211112-2-2-1-1-1-1111122-2-2-2-2-1-1-1-111111111000000000000
χ262222-122222-1-122-12-1-1-1-1-2-2-1-2-221111-1-1-1-1-12-1-1221111-1-1-1-12-2-2-2-211111111-2-211112-2-2-1-1-1-11111-2-222221111-1-1-1-1-1-1-1-1000000000000
χ272222-122-22-2-1-122-12-1-1-1-100-100-2−i3−i3i3i3-1-1-111-21122−i3−i3i3i3-1-1-1-1-22222-1-1-1-1-1-1-1-100−i3−i3i3i3-2001111−i3−i3i3i3-2-200001111−i3−i3i3i3−i3−i3i3i3000000000000
χ282222-122-22-2-1-122-12-1-1-1-100-100-2−i3−i3i3i3-1-1-111-21122−i3−i3i3i3-1-1-1-1-2-2-2-2-21111111100−i3−i3i3i3-2001111−i3−i3i3i3220000-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ292222-122-22-2-1-122-12-1-1-1-100-100-2i3i3−i3−i3-1-1-111-21122i3i3−i3−i3-1-1-1-1-22222-1-1-1-1-1-1-1-100i3i3−i3−i3-2001111i3i3−i3−i3-2-200001111i3i3−i3−i3i3i3−i3−i3000000000000
χ302222-122-22-2-1-122-12-1-1-1-100-100-2i3i3−i3−i3-1-1-111-21122i3i3−i3−i3-1-1-1-1-2-2-2-2-21111111100i3i3−i3−i3-2001111i3i3−i3−i3220000-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ312222-12-22-22-1-122-12111122-1-2-2-2-1-1-1-1-1-1-1-1-1211-2-211111111200003333−3−3−3−322-1-1-1-1-2-2-2-1-111111100000033−3−333−3−3−3−333000000000000
χ322222-12-22-22-1-122-12111122-1-2-2-2-1-1-1-1-1-1-1-1-1211-2-21111111120000−3−3−3−3333322-1-1-1-1-2-2-2-1-1111111000000−3−333−3−33333−3−3000000000000
χ332222-12-22-22-1-122-121111-2-2-122-21111-1-1-1-1-1211-2-2-1-1-1-11111200003333−3−3−3−3-2-21111-222-1-111-1-1-1-100000033−3−3−3−33333−3−3000000000000
χ342222-12-22-22-1-122-121111-2-2-122-21111-1-1-1-1-1211-2-2-1-1-1-1111120000−3−3−3−33333-2-21111-222-1-111-1-1-1-1000000−3−33333−3−3−3−333000000000000
χ352222-12-2-2-2-2-1-122-12111100-1002−i3−i3i3i3-1-1-111-2-1-1-2-2i3i3−i3−i31111-200003333−3−3−3−300−i3−i3i3i320011-1-1i3i3−i3−i3002i2i−2i−2i−3−333−i−i−i−iiiii000000000000
χ362222-12-2-2-2-2-1-122-12111100-1002−i3−i3i3i3-1-1-111-2-1-1-2-2i3i3−i3−i31111-20000−3−3−3−3333300−i3−i3i3i320011-1-1i3i3−i3−i300−2i−2i2i2i33−3−3iiii−i−i−i−i000000000000
χ372222-12-2-2-2-2-1-122-12111100-1002i3i3−i3−i3-1-1-111-2-1-1-2-2−i3−i3i3i31111-200003333−3−3−3−300i3i3−i3−i320011-1-1−i3−i3i3i300−2i−2i2i2i−3−333iiii−i−i−i−i000000000000
χ382222-12-2-2-2-2-1-122-12111100-1002i3i3−i3−i3-1-1-111-2-1-1-2-2−i3−i3i3i31111-20000−3−3−3−3333300i3i3−i3−i320011-1-1−i3−i3i3i3002i2i−2i−2i33−3−3−i−i−i−iiiii000000000000
χ3922-2-222020-22-22-2-2-200002-220002-22-22-2-22-2-20000000000002−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-22-22-20002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-2-222020-22-22-2-2-200002-220002-22-22-2-22-2-20000000000002i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-22-22-20002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4122-2-222020-22-22-2-2-20000-222000-22-222-2-22-2-20000000000002−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-22-22-220002-2000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4222-2-222020-22-22-2-2-20000-222000-22-222-2-22-2-20000000000002i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-22-22-220002-2000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4322-2-2220-2022-22-2-2-200000022i−2i000002-2-2-22200002i−2i2i−2i0000-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000002i−2i-22002i−2i2i−2ii2−i22−2−22i2−i2i2−i22−22−2−22−22000000000000
χ4422-2-2220-2022-22-2-2-200000022i−2i000002-2-2-22200002i−2i2i−2i0000-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000002i−2i-22002i−2i2i−2i−i2i2−222−2−i2i2−i2i2−22−222−22−2000000000000
χ4522-2-2220-2022-22-2-2-20000002−2i2i000002-2-2-2220000−2i2i−2i2i0000-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000−2i2i-2200−2i2i−2i2ii2−i2−222−2i2−i2i2−i2−22−222−22−2000000000000
χ4622-2-2220-2022-22-2-2-20000002−2i2i000002-2-2-2220000−2i2i−2i2i0000-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000−2i2i-2200−2i2i−2i2i−i2i22−2−22−i2i2−i2i22−22−2−22−22000000000000
χ4722-2-2-12020-2-112-21-23−33−32-2-1000-11-11-111-11-23−3003−3−3333−3−32−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ72-2-11-11000-113−33−3−33−i2i2−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4822-2-2-12020-2-112-21-23−33−32-2-1000-11-11-111-11-23−3003−3−3333−3−32i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ72-2-11-11000-113−33−3−33i2−i2i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4922-2-2-12020-2-112-21-23−33−3-22-10001-11-1-111-11-23−300−333−333−3−32−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7-221-11-1000-113−3−333−3−i2i2i2−i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5022-2-2-12020-2-112-21-23−33−3-22-10001-11-1-111-11-23−300−333−333−3−32i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7-221-11-1000-113−3−333−3i2−i2−i2i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5122-2-2-12020-2-112-21-2−33−332-2-1000-11-11-111-11-2−3300−333−3−3−3332−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ232-2-11-11000-11−33−333−3−i2i2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5222-2-2-12020-2-112-21-2−33−332-2-1000-11-11-111-11-2−3300−333−3−3−3332i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ232-2-11-11000-11−33−333−3i2−i2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5322-2-2-12020-2-112-21-2−33−33-22-10001-11-1-111-11-2−33003−3−33−3−3332−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23-221-11-1000-11−333−3−33−i2i2i2−i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5422-2-2-12020-2-112-21-2−33−33-22-10001-11-1-111-11-2−33003−3−33−3−3332i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23-221-11-1000-11−333−3−33i2−i2−i2i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5522-2-2-120-202-112-21-23−33−300-12i−2i0−i3i3i3−i3-1111-12−3300−ii−ii33−3−3-2−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−i3i3i3−i302i−2i1-1−33−ii−iii2−i22−2−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5622-2-2-120-202-112-21-23−33−300-12i−2i0−i3i3i3−i3-1111-12−3300−ii−ii33−3−3-2i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−i3i3i3−i302i−2i1-1−33−ii−ii−i2i2−222−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5722-2-2-120-202-112-21-23−33−300-1−2i2i0i3−i3−i3i3-1111-12−3300i−ii−i33−3−3-2−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700i3−i3−i3i30−2i2i1-1−33i−ii−ii2−i2−222−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5822-2-2-120-202-112-21-23−33−300-1−2i2i0i3−i3−i3i3-1111-12−3300i−ii−i33−3−3-2i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700i3−i3−i3i30−2i2i1-1−33i−ii−i−i2i22−2−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5922-2-2-120-202-112-21-2−33−3300-12i−2i0i3−i3−i3i3-1111-123−300−ii−ii−3−333-2−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300i3−i3−i3i302i−2i1-13−3−ii−iii2−i22−2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ6022-2-2-120-202-112-21-2−33−3300-12i−2i0i3−i3−i3i3-1111-123−300−ii−ii−3−333-2i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300i3−i3−i3i302i−2i1-13−3−ii−ii−i2i2−222−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
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χ1088-8-88-4-400004-44-444−434343−430020000000-22-20000000000023−23−2323000000000000000000000000000000000000000000000000000000000000

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