Finite Group Databasebeta

← Group #11796864

Character table — Group #11796864

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11222222222444444444444444444444448888888888888888888888991818181818242424242424242436363636364848484848484848
order1223344668836668121212121212161616162424242424242424612242424244848484848484848484848484848484844224882244444481616161666121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-11-11-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-11-11-1-111
χ51111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-111111-11-1-1-111
χ81111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-11111-11-1111-1-1
χ911-111-1111-1-111-1-11-1-11111ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111-1-1-1-11-1-11i−ii−i1ii−i−i1-1-11i−ii−i
χ1011-111-1111-1-111-1-11-1-11111ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111-1-1-1-1-111-1−ii−ii1ii−i−i-111-1−ii−ii
χ1111-111-1111-1-111-1-11-1-11111ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1111111-1-1i−i−ii-1−i−iii11-1-1i−i−ii
χ1211-111-1111-1-111-1-11-1-11111ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-11111-1-111−iii−i-1−i−iii-1-111−iii−i
χ1311-111-1111-1-111-1-11-1-11111−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111-1-1-1-11-1-11−ii−ii1−i−iii1-1-11−ii−ii
χ1411-111-1111-1-111-1-11-1-11111−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111-1-1-1-1-111-1i−ii−i1−i−iii-111-1i−ii−i
χ1511-111-1111-1-111-1-11-1-11111−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1111111-1-1−iii−i-1ii−i−i11-1-1−iii−i
χ1611-111-1111-1-111-1-11-1-11111−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-11111-1-111i−i−ii-1ii−i−i-1-111i−i−ii
χ17222222222-2-22222-22222220000-2-2-2-2-2-2-2-222-2-2-2-2000000000000000022222-2-200000000-2000000000000
χ18222222222-2-22222-22222220000-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2-222000000002000000000000
χ1922222-2-2220022220-2-2-2-2-2-22−22−2000000002-200002222−2−2−2−22222−2−2−2−222-2-22000000000002−22−200000000
χ2022222-2-2220022220-2-2-2-2-2-22−22−2000000002-200002222−2−2−2−22222−2−2−2−2-2-222-200000000000−22−2200000000
χ2122222-2-2220022220-2-2-2-2-2-2−22−22000000002-20000−2−2−2−22222−2−2−2−2222222-2-2200000000000−22−2200000000
χ2222222-2-2220022220-2-2-2-2-2-2−22−22000000002-20000−2−2−2−22222−2−2−2−22222-2-222-2000000000002−22−200000000
χ232222-1222-122-1-12-122-12-1-1-1222222-1-1-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1000000002020022000000-10-100-1-1
χ242222-1222-122-1-12-122-12-1-1-1222222-1-1-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-100000000-20-200-2-20000001010011
χ252222-1222-122-1-12-122-12-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-1-1-1-2111-2111-2111-21110000000020200-2-2000000-10-10011
χ262222-1222-122-1-12-122-12-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-1-1-1-2111-2111-2111-211100000000-20-2002200000010100-1-1
χ27222-1222-1222-1-1-122-12-12-1-12222-1-122-1-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-100000002020220000000-10-10-1-100
χ28222-1222-1222-1-1-122-12-12-1-12222-1-122-1-1-1-1-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-10000000-20-20-2-2000000010101100
χ29222-1222-1222-1-1-122-12-12-1-1-2-2-2-2-1-122-1-1-1-1-1-1-12-1-11-2111-2111-2111-21100000002020-2-20000000-10-101100
χ30222-1222-1222-1-1-122-12-12-1-1-2-2-2-2-1-122-1-1-1-1-1-1-12-1-11-2111-2111-2111-2110000000-20-202200000001010-1-100
χ3122-2222-2220022-2-2022-2-2-2-2i2−i2−i2i200000000-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i222-22-200000000000i2−i2−i2i200000000
χ3222-2222-2220022-2-2022-2-2-2-2i2−i2−i2i200000000-220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2-22-2200000000000−i2i2i2−i200000000
χ3322-2222-2220022-2-2022-2-2-2-2−i2i2i2−i200000000-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i222-22-200000000000−i2i2i2−i200000000
χ3422-2222-2220022-2-2022-2-2-2-2−i2i2i2−i200000000-220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2-22-2200000000000i2−i2−i2i200000000
χ3522-222-22222222-2-2-2-2-22222000022222222-2-2-2-2-2-20000000000000000222-2-22200000000-2000000000000
χ3622-222-22222222-2-2-2-2-22222000022222222-2-2-2-2-2-20000000000000000-2-2-222-2-2000000002000000000000
χ3722-22-1-222-1-2-2-1-1-212-212-1-1-12i2i−2i−2i-2-2111111112-1-1-12i−i−i−i2i−i−i−i−2iiii−2iiii0000000020-200−2i2i000000-10100i−i
χ3822-22-1-222-1-2-2-1-1-212-212-1-1-12i2i−2i−2i-2-2111111112-1-1-12i−i−i−i2i−i−i−i−2iiii−2iiii00000000-202002i−2i00000010-100−ii
χ3922-22-1-222-1-2-2-1-1-212-212-1-1-1−2i−2i2i2i-2-2111111112-1-1-1−2iiii−2iiii2i−i−i−i2i−i−i−i0000000020-2002i−2i000000-10100−ii
χ4022-22-1-222-1-2-2-1-1-212-212-1-1-1−2i−2i2i2i-2-2111111112-1-1-1−2iiii−2iiii2i−i−i−i2i−i−i−i00000000-20200−2i2i00000010-100i−i
χ4122-2-12-22-12-2-2-1-11-221-2-12-1-12i2i−2i−2i11-2-2111111-12-1-1−i2i−i−i−i2i−i−ii−2iiii−2iii000000020-202i−2i0000000-1010−ii00
χ4222-2-12-22-12-2-2-1-11-221-2-12-1-12i2i−2i−2i11-2-2111111-12-1-1−i2i−i−i−i2i−i−ii−2iiii−2iii0000000-2020−2i2i000000010-10i−i00
χ4322-2-12-22-12-2-2-1-11-221-2-12-1-1−2i−2i2i2i11-2-2111111-12-1-1i−2iiii−2iii−i2i−i−i−i2i−i−i000000020-20−2i2i0000000-1010i−i00
χ4422-2-12-22-12-2-2-1-11-221-2-12-1-1−2i−2i2i2i11-2-2111111-12-1-1i−2iiii−2iii−i2i−i−i−i2i−i−i0000000-20202i−2i000000010-10−ii00
χ454444-2444-2-4-4-2-24-2-44-24-2-2-20000-4-4222222-2-2-422200000000000000000000000000000000000000000000
χ464444-2-4-44-200-2-24-20-42-422222−2222−2200000000-22000022−2−2−2−2222222−2−2−2−222220000000000000000000000000000
χ474444-2-4-44-200-2-24-20-42-4222−2222−222200000000-220000−2222222−2−2−2−2222222−2−2−20000000000000000000000000000
χ48444-2444-24-4-4-2-2-24-4-24-24-2-2000022-4-42222-2-22-42200000000000000000000000000000000000000000000
χ49444-24-4-4-2400-2-2-2402-42-42222−2222−2200000000-220000−222−2−22−2222−222−2−22−22220000000000000000000000000000
χ50444-24-4-4-2400-2-2-2402-42-422−2222−222200000000-2200002−2222−222−2−22−2222−222−2−20000000000000000000000000000
χ51444-2-244-2-24411-2-24-2-2-2-2114444-2-2-2-2111111-2-211-2-211-2-211-2-211-2-2110000000000000000000000000000
χ52444-2-244-2-24411-2-24-2-2-2-211-4-4-4-4-2-2-2-2111111-2-21122-1-122-1-122-1-122-1-10000000000000000000000000000
χ53444-2-244-2-2-4-411-2-2-4-2-2-2-21100002222-1-1-1-11122-1-1003i−3i003i−3i003i−3i003i−3i0000000000000000000000000000
χ54444-2-244-2-2-4-411-2-2-4-2-2-2-21100002222-1-1-1-11122-1-100−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000000
χ55444-2-2-4-4-2-20011-2-202222-1-122−2222−2200003i3i−3i−3i1-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000000000000000000000000
χ56444-2-2-4-4-2-20011-2-202222-1-122−2222−220000−3i−3i3i3i1-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000000000000000000000000
χ57444-2-2-4-4-2-20011-2-202222-1-1−2222−222200003i3i−3i−3i1-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000000000000000000000000
χ58444-2-2-4-4-2-20011-2-202222-1-1−2222−22220000−3i−3i3i3i1-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000000000000000000000000
χ5944-44-24-44-200-2-2-4204-2-42222i2−2i2−2i22i2000000002-200002i2−i2−i2−i2−2i2i2i2i2−2i2i2i2i22i2−i2−i2−i20000000000000000000000000000
χ6044-44-24-44-200-2-2-4204-2-4222−2i22i22i2−2i2000000002-20000−2i2i2i2i22i2−i2−i2−i22i2−i2−i2−i2−2i2i2i2i20000000000000000000000000000
χ6144-44-2-444-244-2-2-42-4-424-2-2-2000044-2-2-2-2-2-222-422200000000000000000000000000000000000000000000
χ6244-4-244-4-2400-2-22-40-242-4222i2−2i2−2i22i2000000002-20000−i22i2−i2−i2i2−2i2i2i2i2−2i2i2i2−i22i2−i2−i20000000000000000000000000000
χ6344-4-244-4-2400-2-22-40-242-422−2i22i22i2−2i2000000002-20000i2−2i2i2i2−i22i2−i2−i2−i22i2−i2−i2i2−2i2i2i20000000000000000000000000000
χ6444-4-24-44-2444-2-22-4-42-4-24-2-20000-2-244-2-2-2-2222-42200000000000000000000000000000000000000000000
χ6544-4-2-24-4-2-20011220-2-222-1-12i2−2i2−2i22i200003i3i−3i−3i-1100−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000000000000000000000
χ6644-4-2-24-4-2-20011220-2-222-1-12i2−2i2−2i22i20000−3i−3i3i3i-11003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000000000000000000000
χ6744-4-2-24-4-2-20011220-2-222-1-1−2i22i22i2−2i200003i3i−3i−3i-1100−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000000000000000000000
χ6844-4-2-24-4-2-20011220-2-222-1-1−2i22i22i2−2i20000−3i−3i3i3i-11003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000000000000000000000
χ6944-4-2-2-44-2-2441122-422-2-2110000-2-2-2-21111-1-122-1-1003-3003-300-3300-330000000000000000000000000000
χ7044-4-2-2-44-2-2441122-422-2-2110000-2-2-2-21111-1-122-1-100-3300-33003-3003-30000000000000000000000000000
χ7144-4-2-2-44-2-2-4-41122422-2-2114i4i−4i−4i2222-1-1-1-1-1-1-2-211−2i−2iii−2i−2iii2i2i−i−i2i2i−i−i0000000000000000000000000000
χ7244-4-2-2-44-2-2-4-41122422-2-211−4i−4i4i4i2222-1-1-1-1-1-1-2-2112i2i−i−i2i2i−i−i−2i−2iii−2i−2iii0000000000000000000000000000
χ734-404400-4-42i2−2i24-400000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000004i−4i00022−22000000000000000000000
χ744-404400-4-42i2−2i24-400000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000−4i4i000−2222000000000000000000000
χ754-404400-4-4−2i22i24-40000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000004i−4i000−2222000000000000000000000
χ764-404400-4-4−2i22i24-40000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000−4i4i00022−22000000000000000000000
χ778-808-400-844i2−4i2-4400000000000004i2−4i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000000000
χ788-808-400-84−4i24i2-440000000000000−4i24i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000000000
χ798-80-48004-84i2−4i2-440000000000000−2i22i24i2−4i2−2i22i2−2i22i200000000000000000000000000000000000000000000000000
χ808-80-48004-8−4i24i2-4400000000000002i2−2i2−4i24i22i2−2i22i2−2i200000000000000000000000000000000000000000000000000
χ818-80-4-400444i2−4i22-200000006i−6i0000−2i22i2−2i22i24ζ−2ζ3−4ζ+2ζ3−2ζ+4ζ32ζ−4ζ300000000000000000000000000000000000000000000000000
χ828-80-4-400444i2−4i22-20000000−6i6i0000−2i22i2−2i22i2−2ζ+4ζ32ζ−4ζ34ζ−2ζ3−4ζ+2ζ300000000000000000000000000000000000000000000000000
χ838-80-4-40044−4i24i22-200000006i−6i00002i2−2i22i2−2i2−4ζ+2ζ34ζ−2ζ32ζ−4ζ3−2ζ+4ζ300000000000000000000000000000000000000000000000000
χ848-80-4-40044−4i24i22-20000000−6i6i00002i2−2i22i2−2i22ζ−4ζ3−2ζ+4ζ3−4ζ+2ζ34ζ−2ζ300000000000000000000000000000000000000000000000000

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