Finite Group Databasebeta

← Group #11772515

Character table — Group #11772515

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222244444444444444444444488888888888888888888888899181818181836363636367272727272727272
order122448833668121212121616161624242424242424246612122424242448484848484848484848484848484848442248881616161688888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ51111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111-1-1-1-11ii−i−i1-11-1i−ii−i
χ1011-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111-1-1-1-11ii−i−i-11-11−ii−ii
χ1111-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-11111-1−i−iiii−i−ii-111-1
χ1211-1-11-1-1111111111ii−i−i-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-11111-1−i−iii−iii−i1-1-11
χ1311-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111-1-1-1-11−i−iii1-11-1−ii−ii
χ1411-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111-1-1-1-11−i−iii-11-11i−ii−i
χ1511-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-11111-1ii−i−ii−i−ii1-1-11
χ1611-1-11-1-1111111111−i−iii-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-11111-1ii−i−i−iii−i-111-1
χ1722222-2-22222-222220000-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000022222-2-2-2000000000000
χ1822222-2-22222-222220000-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2-2-2-2222000000000000
χ19222-2-20022220-2-2-2-22−22−20000000022-2-200002222−2−2−2−22222−2−2−2−222-2-220002−22−200000000
χ20222-2-20022220-2-2-2-22−22−20000000022-2-200002222−2−2−2−22222−2−2−2−2-2-222-2000−22−2200000000
χ21222-2-20022220-2-2-2-2−22−220000000022-2-20000−2−2−2−22222−2−2−2−2222222-2-22000−22−2200000000
χ22222-2-20022220-2-2-2-2−22−220000000022-2-20000−2−2−2−22222−2−2−2−22222-2-222-20002−22−200000000
χ2322-22-20022220-2-2-2-2i2−i2−i2i200000000-2-2220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i222-22-2000i2−i2−i2i200000000
χ2422-22-20022220-2-2-2-2i2−i2−i2i200000000-2-2220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2-22-22000−i2i2i2−i200000000
χ2522-22-20022220-2-2-2-2−i2i2i2−i200000000-2-2220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i222-22-2000−i2i2i2−i200000000
χ2622-22-20022220-2-2-2-2−i2i2i2−i200000000-2-2220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2-22-22000i2−i2−i2i200000000
χ2722-2-22222222-22222000022222222-2-2-2-2-2-2-2-20000000000000000222-2-222-2000000000000
χ2822-2-22222222-22222000022222222-2-2-2-2-2-2-2-20000000000000000-2-2-222-2-22000000000000
χ2944444441-21-2411-2-244441111-2-2-2-21-21-211-2-211-2-211-2-211-2-211-2-200000000000000000000
χ3044444441-21-2411-2-2-4-4-4-41111-2-2-2-21-21-211-2-2-1-122-1-122-1-122-1-12200000000000000000000
χ314444444-21-214-2-2114444-2-2-2-21111-21-21-2-211-2-211-2-211-2-211-2-21100000000000000000000
χ324444444-21-214-2-211-4-4-4-4-2-2-2-21111-21-21-2-21122-1-122-1-122-1-122-1-100000000000000000000
χ3344444-4-41-21-2-411-2-20000-1-1-1-122221-21-2-1-1223i−3i003i−3i003i−3i003i−3i0000000000000000000000
χ3444444-4-41-21-2-411-2-20000-1-1-1-122221-21-2-1-122−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000
χ3544444-4-4-21-21-4-2-21100002222-1-1-1-1-21-2122-1-1003i−3i003i−3i003i−3i003i−3i00000000000000000000
χ3644444-4-4-21-21-4-2-21100002222-1-1-1-1-21-2122-1-100−3i3i00−3i3i00−3i3i00−3i3i00000000000000000000
χ37444-4-4001-21-20-1-12222−2222−223i3i−3i−3i00001-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ32200000000000000000000
χ38444-4-4001-21-20-1-12222−2222−22−3i−3i3i3i00001-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ32200000000000000000000
χ39444-4-4001-21-20-1-122−2222−22223i3i−3i−3i00001-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−200000000000000000000
χ40444-4-4001-21-20-1-122−2222−2222−3i−3i3i3i00001-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−200000000000000000000
χ41444-4-400-21-21022-1-122−2222−2200003i3i−3i−3i-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ300000000000000000000
χ42444-4-400-21-21022-1-122−2222−220000−3i−3i3i3i-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ300000000000000000000
χ43444-4-400-21-21022-1-1−2222−222200003i3i−3i−3i-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ300000000000000000000
χ44444-4-400-21-21022-1-1−2222−22220000−3i−3i3i3i-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ300000000000000000000
χ4544-44-4001-21-20-1-1222i2−2i2−2i22i23i3i−3i−3i0000-121-2−3i3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i200000000000000000000
χ4644-44-4001-21-20-1-1222i2−2i2−2i22i2−3i−3i3i3i0000-121-23i−3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i200000000000000000000
χ4744-44-4001-21-20-1-122−2i22i22i2−2i23i3i−3i−3i0000-121-2−3i3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i200000000000000000000
χ4844-44-4001-21-20-1-122−2i22i22i2−2i2−3i−3i3i3i0000-121-23i−3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i200000000000000000000
χ4944-44-400-21-21022-1-12i2−2i2−2i22i200003i3i−3i−3i2-1-2100−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ300000000000000000000
χ5044-44-400-21-21022-1-12i2−2i2−2i22i20000−3i−3i3i3i2-1-21003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ300000000000000000000
χ5144-44-400-21-21022-1-1−2i22i22i2−2i200003i3i−3i−3i2-1-2100−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ300000000000000000000
χ5244-44-400-21-21022-1-1−2i22i22i2−2i20000−3i−3i3i3i2-1-21003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ300000000000000000000
χ5344-4-44441-21-2-411-2-200001111-2-2-2-2-12-12-1-1223-3003-300-3300-330000000000000000000000
χ5444-4-44441-21-2-411-2-200001111-2-2-2-2-12-12-1-122-3300-33003-3003-30000000000000000000000
χ5544-4-4444-21-21-4-2-2110000-2-2-2-211112-12-122-1-1003-3003-300-3300-3300000000000000000000
χ5644-4-4444-21-21-4-2-2110000-2-2-2-211112-12-122-1-100-3300-33003-3003-300000000000000000000
χ5744-4-44-4-41-21-2411-2-24i4i−4i−4i-1-1-1-12222-12-1211-2-2ii−2i−2iii−2i−2i−i−i2i2i−i−i2i2i00000000000000000000
χ5844-4-44-4-41-21-2411-2-2−4i−4i4i4i-1-1-1-12222-12-1211-2-2−i−i2i2i−i−i2i2iii−2i−2iii−2i−2i00000000000000000000
χ5944-4-44-4-4-21-214-2-2114i4i−4i−4i2222-1-1-1-12-12-1-2-211−2i−2iii−2i−2iii2i2i−i−i2i2i−i−i00000000000000000000
χ6044-4-44-4-4-21-214-2-211−4i−4i4i4i2222-1-1-1-12-12-1-2-2112i2i−i−i2i2i−i−i−2i−2iii−2i−2iii00000000000000000000
χ614-40002i2−2i244-4-40000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000004i−4i00022−220000000000000
χ624-40002i2−2i244-4-40000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000−4i4i000−22220000000000000
χ634-4000−2i22i244-4-4000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000004i−4i000−22220000000000000
χ644-4000−2i22i244-4-4000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000−4i4i00022−220000000000000
χ658-80004i2−4i22-4-2406i−6i0000004ζ−2ζ3−4ζ+2ζ3−2ζ+4ζ32ζ−4ζ3−2i22i2−2i22i200000000000000000000000000000000000000000000
χ668-80004i2−4i22-4-240−6i6i000000−2ζ+4ζ32ζ−4ζ34ζ−2ζ3−4ζ+2ζ3−2i22i2−2i22i200000000000000000000000000000000000000000000
χ678-80004i2−4i2-424-20006i−6i0000−2i22i2−2i22i24ζ−2ζ3−4ζ+2ζ3−2ζ+4ζ32ζ−4ζ300000000000000000000000000000000000000000000
χ688-80004i2−4i2-424-2000−6i6i0000−2i22i2−2i22i2−2ζ+4ζ32ζ−4ζ34ζ−2ζ3−4ζ+2ζ300000000000000000000000000000000000000000000
χ698-8000−4i24i22-4-2406i−6i000000−4ζ+2ζ34ζ−2ζ32ζ−4ζ3−2ζ+4ζ32i2−2i22i2−2i200000000000000000000000000000000000000000000
χ708-8000−4i24i22-4-240−6i6i0000002ζ−4ζ3−2ζ+4ζ3−4ζ+2ζ34ζ−2ζ32i2−2i22i2−2i200000000000000000000000000000000000000000000
χ718-8000−4i24i2-424-20006i−6i00002i2−2i22i2−2i2−4ζ+2ζ34ζ−2ζ32ζ−4ζ3−2ζ+4ζ300000000000000000000000000000000000000000000
χ728-8000−4i24i2-424-2000−6i6i00002i2−2i22i2−2i22ζ−4ζ3−2ζ+4ζ3−4ζ+2ζ34ζ−2ζ300000000000000000000000000000000000000000000

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