Finite Group Databasebeta

← Group #11776244

Character table — Group #11776244

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222244444444444444444444488888888888888888888889999121212121212121218181818242424242424242424242424363636363648484848
order1222334444666666346668888121212121212121212121212121212121212242424242424242424242424242424244444888888884444444424242424242424242888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111
χ5111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111
χ7111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-111
χ8111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1111111-1-1
χ9111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111ii−i−iii−i−i-1-1-1-11-11-1ii−i−iii−i−i1ii−i−i1-11-1
χ10111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111−i−iii−i−iii-1-1-1-1-11-11−i−iii−i−iii1ii−i−i-11-11
χ11111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1ii−i−i−i−iii11111-1-11ii−i−i−i−iii-1−i−iii1-1-11
χ12111111-1-1-1-111111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1−i−iiiii−i−i1111-111-1−i−iiiii−i−i-1−i−iii-111-1
χ13111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111ii−i−iii−i−i-1-1-1-1-11-11ii−i−iii−i−i1−i−iii-11-11
χ14111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111−i−iii−i−iii-1-1-1-11-11-1−i−iii−i−iii1−i−iii1-11-1
χ15111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1ii−i−i−i−iii1111-111-1ii−i−i−i−iii-1ii−i−i-111-1
χ16111111-1-1-1-111111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−iiiii−i−i11111-1-11−i−iiiii−i−i-1ii−i−i1-1-11
χ172222222-2-222222222-222200002-22-2222222-2-2-2-2-2-2-2-2000000000000000022220000000022-2-2000000000000-200000000
χ182222222-2-222222222-222200002-22-2222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-200000000-2-222000000000000200000000
χ19222222-222-22222222-22220000-22-22-2-2-2-2-2-222-2-2-2-2220000000000000000222200000000-2-222000000000000-200000000
χ20222222-222-22222222-22220000-22-22-2-2-2-2-2-222-2-2-2-2220000000000000000-2-2-2-20000000022-2-2000000000000200000000
χ2122222-1222222-1-12-1-12-1-1-122222-1-12-1-12-1-1-1-122-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000002222000000220000-1-1-1-10000000-1-1
χ2222222-1222222-1-12-1-12-1-1-122222-1-12-1-12-1-1-1-122-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-2000000-2-200001111000000011
χ2322222-1222222-1-12-1-12-1-1-1-2-2-2-22-1-12-1-12-1-1-1-122-1-1-1-1-1-2-2111111-2-2111111000000002222000000-2-20000-1-1-1-1000000011
χ2422222-1222222-1-12-1-12-1-1-1-2-2-2-22-1-12-1-12-1-1-1-122-1-1-1-1-1-2-2111111-2-211111100000000-2-2-2-200000022000011110000000-1-1
χ2522222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-211-211-21111-22-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii000000002i2i−2i−2i0000002-20000−i−iii0000000-11
χ2622222-1-2-2-2-222-1-12-1-12-1-1-12i2i−2i−2i-211-211-21111-22-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00000000−2i−2i2i2i000000-220000ii−i−i00000001-1
χ2722222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-211-211-21111-22-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000002i2i−2i−2i000000-220000−i−iii00000001-1
χ2822222-1-2-2-2-222-1-12-1-12-1-1-1−2i−2i2i2i-211-211-21111-22-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000−2i−2i2i2i0000002-20000ii−i−i0000000-11
χ292222-122222-1-122-12-12-1-1-12222-122-1-1-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100002222000000002200-1-1-1-1000000000-1-100
χ302222-122222-1-122-12-12-1-1-12222-122-1-1-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-200000000-2-20011110000000001100
χ312222-122222-1-122-12-12-1-1-1-2-2-2-2-122-1-1-1-12-1-12-1-12-1-1-1-111-2-2111111-2-211110000222200000000-2-200-1-1-1-10000000001100
χ322222-122222-1-122-12-12-1-1-1-2-2-2-2-122-1-1-1-12-1-12-1-12-1-1-1-111-2-2111111-2-211110000-2-2-2-20000000022001111000000000-1-100
χ332222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-2-21111-211-21-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii00002i2i−2i−2i000000002-200−i−iii000000000-1100
χ342222-12-2-2-2-2-1-122-12-12-1-1-12i2i−2i−2i1-2-21111-211-21-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii0000−2i−2i2i2i00000000-2200ii−i−i0000000001-100
χ352222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-2-21111-211-21-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i00002i2i−2i−2i00000000-2200−i−iii0000000001-100
χ362222-12-2-2-2-2-1-122-12-12-1-1-1−2i−2i2i2i1-2-21111-211-21-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000−2i−2i2i2i000000002-200ii−i−i000000000-1100
χ372-22-22202-20-2-22-22-2202-2-2i2−i2i2−i20-2020000002-200002-2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i22i2i−2i−2i00000000002i−2i00000000000002−22−20000
χ382-22-22202-20-2-22-22-2202-2-2i2−i2i2−i20-2020000002-200002-2i2−i2i2−i2i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2−2i−2i2i2i0000000000−2i2i0000000000000−22−220000
χ392-22-22202-20-2-22-22-2202-2-2−i2i2−i2i20-2020000002-200002-2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i22i2i−2i−2i00000000002i−2i0000000000000−22−220000
χ402-22-22202-20-2-22-22-2202-2-2−i2i2−i2i20-2020000002-200002-2−i2i2−i2i2−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−2i−2i2i2i0000000000−2i2i00000000000002−22−20000
χ412-22-2220-220-2-22-22-2202-2-22−2−22020-2000000-220000-222−22−222−2−2−22−22−2−2222i2i−2i−2i0000000000−2i2i0000000000000−i2i2i2−i20000
χ422-22-2220-220-2-22-22-2202-2-22−2−22020-2000000-220000-222−22−222−2−2−22−22−2−222−2i−2i2i2i00000000002i−2i0000000000000i2−i2−i2i20000
χ432-22-2220-220-2-22-22-2202-2-2−222−2020-2000000-220000-22−22−22−2−2222−22−222−2−22i2i−2i−2i0000000000−2i2i0000000000000i2−i2−i2i20000
χ442-22-2220-220-2-22-22-2202-2-2−222−2020-2000000-220000-22−22−22−2−2222−22−222−2−2−2i−2i2i2i00000000002i−2i0000000000000−i2i2i2−i20000
χ452-2-2222200-22-2-2-2-2220-22-20000-20-20-2-222220000000000000000000000002i−2i2i−2ii2−i2i2−i22−22−22i−2i000000i2−i2i2−i22−22−2000000000
χ462-2-2222200-22-2-2-2-2220-22-20000-20-20-2-222220000000000000000000000002i−2i2i−2i−i2i2−i2i2−22−222i−2i000000−i2i2−i2i2−22−22000000000
χ472-2-2222200-22-2-2-2-2220-22-20000-20-20-2-22222000000000000000000000000−2i2i−2i2ii2−i2i2−i2−22−22−2i2i000000i2−i2i2−i2−22−22000000000
χ482-2-2222200-22-2-2-2-2220-22-20000-20-20-2-22222000000000000000000000000−2i2i−2i2i−i2i2−i2i22−22−2−2i2i000000−i2i2−i2i22−22−2000000000
χ492-2-2222-20022-2-2-2-2220-22-20000202022-2-2-2-20000000000000000000000002i−2i2i−2i2−2−22−i2i2i2−i2−2i2i0000002−2−22−i2i2i2−i2000000000
χ502-2-2222-20022-2-2-2-2220-22-20000202022-2-2-2-20000000000000000000000002i−2i2i−2i−222−2i2−i2−i2i2−2i2i000000−222−2i2−i2−i2i2000000000
χ512-2-2222-20022-2-2-2-2220-22-20000202022-2-2-2-2000000000000000000000000−2i2i−2i2i2−2−22i2−i2−i2i22i−2i0000002−2−22i2−i2−i2i2000000000
χ522-2-2222-20022-2-2-2-2220-22-20000202022-2-2-2-2000000000000000000000000−2i2i−2i2i−222−2−i2i2i2−i22i−2i000000−222−2−i2i2i2−i2000000000
χ5344444-24-4-4444-2-24-2-2-4-2-2-2000042-2-4-2-24-2-2-22-4-42222200000000000000000000000000000000000000000000000000000
χ5444444-2-444-444-2-24-2-2-4-2-2-20000-4-22422-4222-24-4222-2-200000000000000000000000000000000000000000000000000000
χ554444-244-4-44-2-244-24-2-4-2-2-20000-2-442-2-2-24-2-2-422-4222200000000000000000000000000000000000000000000000000000
χ564444-24-444-4-2-244-24-2-4-2-2-2000024-4-2222-4224-22-422-2-200000000000000000000000000000000000000000000000000000
χ574444-2-24444-2-2-2-2-2-2141114444-2-2-2-211-2-211-2-2-2-21111-2-2-2-21111-2-2-2-211110000000000000000000000000000000000000
χ584444-2-24444-2-2-2-2-2-214111-4-4-4-4-2-2-2-211-2-211-2-2-2-211112222-1-1-1-12222-1-1-1-10000000000000000000000000000000000000
χ594444-2-24-4-44-2-2-2-2-2-21-41110000-22-2211-2-2112222-1-1-1-100003-33-300003-33-30000000000000000000000000000000000000
χ604444-2-24-4-44-2-2-2-2-2-21-41110000-22-2211-2-2112222-1-1-1-10000-33-330000-33-330000000000000000000000000000000000000
χ614444-2-2-444-4-2-2-2-2-2-21-411100002-22-2-1-122-1-1-2-222-1-11100003i−3i3i−3i0000−3i3i−3i3i0000000000000000000000000000000000000
χ624444-2-2-444-4-2-2-2-2-2-21-411100002-22-2-1-122-1-1-2-222-1-1110000−3i3i−3i3i00003i−3i3i−3i0000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-2141114i4i−4i−4i2222-1-122-1-122-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-214111−4i−4i4i4i2222-1-122-1-122-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000000000
χ6544-4-4440000-44-44-4-440-4-44000000000000000000000000000000000000004-4-44000000000000000000000000000000000
χ6644-4-4440000-44-44-4-440-4-4400000000000000000000000000000000000000-444-4000000000000000000000000000000000
χ674-44-44-204-40-4-4-2242-20-2222i2−2i22i2−2i20204000000-2-40000-222i2−2i2−i2i2−i2−i2i2i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000000000000
χ684-44-44-204-40-4-4-2242-20-222−2i22i2−2i22i20204000000-2-40000-22−2i22i2i2−i2i2i2−i2−i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000000000000
χ694-44-44-20-440-4-4-2242-20-22222−22−22220-20-40000002400002-222−22−22−2−222−22222−222−2−20000000000000000000000000000000000000
χ704-44-44-20-440-4-4-2242-20-222−222222−220-20-40000002400002-2−22222−222−2−222−22−22−2−2220000000000000000000000000000000000000
χ714-44-4-2404-40224-4-2-4-20-2222i2−2i22i2−2i20-40-2000000420000-22−i2i22i2−2i2−i2−i2i2i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000000000000
χ724-44-4-2404-40224-4-2-4-20-222−2i22i2−2i22i20-40-2000000420000-22i2−i2−2i22i2i2i2−i2−i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000000000000
χ734-44-4-240-440224-4-2-4-20-22222−22−22220402000000-4-200002-2−2222−22−2−2222−2−222222−2−20000000000000000000000000000000000000
χ744-44-4-240-440224-4-2-4-20-222−222222−220402000000-4-200002-22−2−222222−2−2−2222−22−2−2220000000000000000000000000000000000000
χ754-44-4-2-204-4022-22-22101-1-12i2−2i22i2−2i2020-23i−3i003i−3i-22003i−3i1-1−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ3−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ30000000000000000000000000000000000000
χ764-44-4-2-204-4022-22-22101-1-12i2−2i22i2−2i2020-2−3i3i00−3i3i-2200−3i3i1-1−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ30000000000000000000000000000000000000
χ774-44-4-2-204-4022-22-22101-1-1−2i22i2−2i22i2020-23i−3i003i−3i-22003i−3i1-1i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ3i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ30000000000000000000000000000000000000
χ784-44-4-2-204-4022-22-22101-1-1−2i22i2−2i22i2020-2−3i3i00−3i3i-2200−3i3i1-1i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ30000000000000000000000000000000000000
χ794-44-4-2-20-44022-22-22101-1-122−22−22220-2023i−3i003i−3i2-200−3i3i-11−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000000000000000000000
χ804-44-4-2-20-44022-22-22101-1-122−22−22220-202−3i3i00−3i3i2-2003i−3i-11−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000000000000000000000
χ814-44-4-2-20-44022-22-22101-1-1−222222−220-2023i−3i003i−3i2-200−3i3i-112−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000000000000000000000
χ824-44-4-2-20-44022-22-22101-1-1−222222−220-202−3i3i00−3i3i2-2003i−3i-112−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000000000000000000000
χ834-4-444-2400-44-422-4-2-202-220000-4020224-2-2-20000000000000000000000000000000022−2222−22000000000000−22−22000000000
χ844-4-444-2400-44-422-4-2-202-220000-4020224-2-2-200000000000000000000000000000000−2222−22220000000000002−22−2000000000
χ854-4-444-2-40044-422-4-2-202-22000040-20-2-2-4222000000000000000000000000000000002i2−2i2−2i22i2000000000000−i2i2i2−i2000000000
χ864-4-444-2-40044-422-4-2-202-22000040-20-2-2-422200000000000000000000000000000000−2i22i22i2−2i2000000000000i2−i2−i2i2000000000
χ874-4-44-24400-4-22-4-424-202-22000020-4022-24-2-200000000000000000000000000002i2−2i22i2−2i2000000000000−i2i2−i2i20000000000000
χ884-4-44-24400-4-22-4-424-202-22000020-4022-24-2-20000000000000000000000000000−2i22i2−2i22i2000000000000i2−i2i2−i20000000000000
χ894-4-44-24-4004-22-4-424-202-220000-2040-2-22-422000000000000000000000000000022−22−2222000000000000−222−20000000000000
χ904-4-44-24-4004-22-4-424-202-220000-2040-2-22-4220000000000000000000000000000−222222−220000000000002−2−220000000000000
χ9188-8-88-40000-884-4-84-4044-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4800004-4-884-8-4044-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-400004-44-44420-2-22000000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-400004-44-44420-2-2200000000−6i6i006i−6i0000000000000000000000000000000000000000000000000000000000000
χ958-8-88-4-4800-8-44444-420-22-200004040-2-2-4-4220000000000000000000000000000000000000000000000000000000000000
χ968-8-88-4-4-8008-44444-420-22-20000-40-402244-2-20000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.