Finite Group Databasebeta

← Group #11775360

Character table — Group #11775360

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888181824242424242424242424242424242424363636484848487272
order1222223344666666346666666666612121212441212121212121212121212121212121212121212121244244488882424242424242424444612121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111111-1-11-11-111-1-11111-1-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-11-11-1-111-1-1-1-11111-1-1-1-1-111-1-1
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-1-11111
χ91111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i111-1-11i−ii−iii−i−iii−i−i1-1-11-11-1i−i
χ101111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-111-1−ii−ii−i−iii−i−iii1-1-1-11-11i−i
χ111111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1i−i−iiii−i−i−i−iii-1111-1-11−ii
χ121111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−iii−i−i−iiiii−i−i-111-111-1−ii
χ131111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii111-1-11−ii−ii−i−iii−i−iii1-1-11-11-1−ii
χ141111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-111-1i−ii−iii−i−iii−i−i1-1-1-11-11−ii
χ151111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1−iii−i−i−iiiii−i−i-1111-1-11i−i
χ161111-1-111-1-111111111-1-111-1-1-1-11-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111i−i−iiii−i−i−i−iii-111-111-1i−i
χ1722222222-2-22222222-222222222222-2-2-2-200-2-2-2-2-2-20000000000000000220000000000000000-22-2000000
χ1822222222-2-22222222-222222222222-2-2-2-200-2-2-2-2-2-20000000000000000-2-200000000000000002-22000000
χ192222222-1222-1-12-12-122-1-1-1-1-12-1-1-1-1-1-12222-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10020202200-1-1-1-10000000-1-10000
χ202222222-1222-1-12-12-122-1-1-1-1-12-1-1-1-1-1-12222-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100-20-20-2-20011110000000110000
χ212222222-1222-1-12-12-122-1-1-1-1-12-1-1-1-1-1-122-2-2-12-1-1-1-1-2-2111111-2-2111111002020-2-20011110000000-1-10000
χ222222222-1222-1-12-12-122-1-1-1-1-12-1-1-1-1-1-122-2-2-12-1-1-1-1-2-2111111-2-211111100-20-202200-1-1-1-10000000110000
χ23222222-1222-122-12-1-12-12-1-1-1-1-12-1-1-122-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100020200220000-1-1-1-100000-1-100
χ24222222-1222-122-12-1-12-12-1-1-1-1-12-1-1-122-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000-20-200-2-200001111000001100
χ25222222-1222-122-12-1-12-12-1-1-1-1-12-1-1-122-1-1-2-22-1-1-1-1-111-2-2111111-2-2111100020200-2-20000111100000-1-100
χ26222222-1222-122-12-1-12-12-1-1-1-1-12-1-1-122-1-1-2-22-1-1-1-1-111-2-2111111-2-21111000-20-200220000-1-1-1-1000001100
χ272222-2-222222222222-2-2-222-2-2-2-22-2-2222200-2-2-2-2220000000000000000220000000000000000-2-22000000
χ282222-2-222222222222-2-2-222-2-2-2-22-2-2222200-2-2-2-2220000000000000000-2-2000000000000000022-2000000
χ292222-2-22-1-2-22-1-12-12-12-21-1-111-21-11111-2-22i−2i-12-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii0020-202i−2i00−i−iii0000000-110000
χ302222-2-22-1-2-22-1-12-12-12-21-1-111-21-11111-2-22i−2i-12-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00-2020−2i2i00ii−i−i00000001-10000
χ312222-2-22-1-2-22-1-12-12-12-21-1-111-21-11111-2-2−2i2i-12-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i0020-20−2i2i00ii−i−i0000000-110000
χ322222-2-22-1-2-22-1-12-12-12-21-1-111-21-11111-2-2−2i2i-12-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00-20202i−2i00−i−iii00000001-10000
χ332222-2-2-12-2-2-122-12-1-121-2-1-1111-2-111-2-2112i−2i2-1-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii00020-200−2i2i0000ii−i−i000001-100
χ342222-2-2-12-2-2-122-12-1-121-2-1-1111-2-111-2-2112i−2i2-1-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii000-202002i−2i0000−i−iii00000-1100
χ352222-2-2-12-2-2-122-12-1-121-2-1-1111-2-111-2-211−2i2i2-1-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i00020-2002i−2i0000−i−iii000001-100
χ362222-2-2-12-2-2-122-12-1-121-2-1-1111-2-111-2-211−2i2i2-1-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i000-20200−2i2i0000ii−i−i00000-1100
χ374444444-2-4-44-2-24-24-2-44-2-2-2-2-24-2-2-2-222-4-4002-422220000000000000000000000000000000000000000000
χ38444444-24-4-4-244-24-2-2-4-24-2-2-2-2-24-2-2-2-4-42200-4222220000000000000000000000000000000000000000000
χ39444444-2-244-2-2-2-2-2-214-2-21111-2-2111-2-2-2-244-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000
χ40444444-2-244-2-2-2-2-2-214-2-21111-2-2111-2-2-2-2-4-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000
χ41444444-2-2-4-4-2-2-2-2-2-21-4-2-21111-2-211122220022-1-1-1-1000033-3-3000033-3-3000000000000000000000000000
χ42444444-2-2-4-4-2-2-2-2-2-21-4-2-21111-2-211122220022-1-1-1-10000-3-3330000-3-333000000000000000000000000000
χ434444-4-44-2444-2-24-24-2-4-42-2-222-42-222-2-244002-422-2-20000000000000000000000000000000000000000000
χ444444-4-4-2444-244-24-2-2-42-4-2-2222-4-22244-2-200-4222-2-20000000000000000000000000000000000000000000
χ454444-4-4-2-244-2-2-2-2-2-21-42211-1-1221-1-1-2-2-2-20022-1-11100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000
χ464444-4-4-2-244-2-2-2-2-2-21-42211-1-1221-1-1-2-2-2-20022-1-1110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000
χ474444-4-4-2-2-4-4-2-2-2-2-2-2142211-1-1221-1-122224i−4i-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000
χ484444-4-4-2-2-4-4-2-2-2-2-2-2142211-1-1221-1-12222−4i4i-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000
χ4944-4-4004400-4-44-4-444000-4-4000040000000000000000000000000000004i−4i0000000000000000000000000
χ5044-4-4004400-4-44-4-444000-4-400004000000000000000000000000000000−4i4i0000000000000000000000000
χ514-44-400444i−4i-44-44-4-440004-40000-4004i−4i4i−4i0000004i−4i0000000000000000000000000000000000000000000
χ524-44-40044−4i4i-44-44-4-440004-40000-400−4i4i−4i4i000000−4i4i0000000000000000000000000000000000000000000
χ534-44-4004-24i−4i-4-2242-4-2000-220000200−2i2i4i−4i000000−2i2i00−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000000
χ544-44-4004-24i−4i-4-2242-4-2000-220000200−2i2i4i−4i000000−2i2i00ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000000
χ554-44-4004-2−4i4i-4-2242-4-2000-2200002002i−2i−4i4i0000002i−2i00−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000000
χ564-44-4004-2−4i4i-4-2242-4-2000-2200002002i−2i−4i4i0000002i−2i00ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000000
χ574-44-400-244i−4i24-4-2-42-2000-2200002004i−4i−2i2i000000−2i2i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000000
χ584-44-400-244i−4i24-4-2-42-2000-2200002004i−4i−2i2i000000−2i2iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000000
χ594-44-400-24−4i4i24-4-2-42-2000-220000200−4i4i2i−2i0000002i−2i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000000
χ604-44-400-24−4i4i24-4-2-42-2000-220000200−4i4i2i−2i0000002i−2iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000000
χ614-44-400-2-24i−4i2-22-22210001-13-300-13-3−2i2i−2i2i00003i−3ii−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22i3−i3−33−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22i3−i33−3000000000000000000000000000
χ624-44-400-2-24i−4i2-22-22210001-13-300-13-3−2i2i−2i2i00003i−3ii−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−i3i33−3ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−i3i3−33000000000000000000000000000
χ634-44-400-2-24i−4i2-22-22210001-1-3300-1-33−2i2i−2i2i0000−3i3ii−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ223−3−i3i3−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−33−i3i3000000000000000000000000000
χ644-44-400-2-24i−4i2-22-22210001-1-3300-1-33−2i2i−2i2i0000−3i3ii−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−33i3−i3ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ223−3i3−i3000000000000000000000000000
χ654-44-400-2-2−4i4i2-22-22210001-13-300-13-32i−2i2i−2i0000−3i3i−ii−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22i3−i33−3−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22i3−i3−33000000000000000000000000000
χ664-44-400-2-2−4i4i2-22-22210001-13-300-13-32i−2i2i−2i0000−3i3i−iiζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−i3i3−33ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−i3i33−3000000000000000000000000000
χ674-44-400-2-2−4i4i2-22-22210001-1-3300-1-332i−2i2i−2i00003i−3i−ii−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−33−i3i3−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ223−3−i3i3000000000000000000000000000
χ684-44-400-2-2−4i4i2-22-22210001-1-3300-1-332i−2i2i−2i00003i−3i−iiζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ223−3i3−i3ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−33i3−i3000000000000000000000000000
χ694-4-444-444004-4-4-44-44044-4444-4-4-4-4-40000000000000000000000000000000000000000000000000000000
χ704-4-444-44-200422-4-2-4-204-22-2-2-2-42222000000000000000000000000000000000000006−66−60000000000000
χ714-4-444-44-200422-4-2-4-204-22-2-2-2-4222200000000000000000000000000000000000000−66−660000000000000
χ724-4-444-4-2400-2-4-4242-20-242-2-2-22-4222000000000000000000000000000000000000000000i6−i6i6−i6000000000
χ734-4-444-4-2400-2-4-4242-20-242-2-2-22-4222000000000000000000000000000000000000000000−i6i6−i6i6000000000
χ744-4-44-4444004-4-4-44-440-4-4-44-4-444-4440000000000000000000000000000000000000000000000000000000
χ754-4-44-444-200422-4-2-4-20-422-2224-22-2-200000000000000000000000000000000000000i6−i6−i6i60000000000000
χ764-4-44-444-200422-4-2-4-20-422-2224-22-2-200000000000000000000000000000000000000−i6i6i6−i60000000000000
χ774-4-44-44-2400-2-4-4242-202-42-222-242-2-20000000000000000000000000000000000000000006−6−66000000000
χ784-4-44-44-2400-2-4-4242-202-42-222-242-2-2000000000000000000000000000000000000000000−666−6000000000
χ7988-8-8008-400-84-4-848-4000440000-4000000000000000000000000000000000000000000000000000000000
χ8088-8-800-48004-884-8-4-4000440000-4000000000000000000000000000000000000000000000000000000000
χ8188-8-800-4-40044-444-42000-2-26-6002-660000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-40044-444-42000-2-2-660026-60000000000000000000000000000000000000000000000000000000
χ838-8-888-8-4-400-4444-4420-4-4-222244-2-2-20000000000000000000000000000000000000000000000000000000
χ848-8-88-88-4-400-4444-442044-22-2-2-4-4-2220000000000000000000000000000000000000000000000000000000

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