Finite Group Databasebeta

← Group #11867870

Character table — Group #11867870

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11222222222444444444444444444444448888888888888888888888991818181818242424242424242436363636364848484848484848
order1223344668823466688812121212121224242424242424246666612121212122424242424242424242424242224488224488882488866121224242424
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
χ511111111111-11-11111-1-111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11-1-11111-1-1-1-1
χ611111111111-11-11111-1-111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-11-1-1-1-1-1-11111
χ711111111111-11-11111-1-111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1111-11-1-1-111
χ811111111111-11-11111-1-111111111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-111-11-1111-1-1
χ9111111111-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-11-11-111-1-1-111-1-11-11-1
χ10111111111-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11-1111-1-1-1-1-111-11-11
χ11111111111-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-11111-1-111-1-11
χ12111111111-1-1111111-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1111-111-1-111-1
χ13111111111-1-1-11-1111-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111111111111-1-111-1-1-11-11-1-1-11111-1-1-11-11
χ14111111111-1-1-11-1111-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111111111111-1-1-1-1111-11-1-1-1-111-1-1111-11-1
χ15111111111-1-1-11-1111-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1111-1-11-111-1111-1-11-1-11-111-1
χ16111111111-1-1-11-1111-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-111-111-11-1-11111-1-1-111-11-1-11
χ1722222-2-2220002022202i−2i-2-2-2-2-2-2000000000020000-20000002i2i2i2i−2i−2i−2i−2i222-2-200000000000002i−2i00000000
χ1822222-2-2220002022202i−2i-2-2-2-2-2-2000000000020000-20000002i2i2i2i−2i−2i−2i−2i-2-2-2220000000000000−2i2i00000000
χ1922222-2-222000202220−2i2i-2-2-2-2-2-2000000000020000-2000000−2i−2i−2i−2i2i2i2i2i222-2-20000000000000−2i2i00000000
χ2022222-2-222000202220−2i2i-2-2-2-2-2-2000000000020000-2000000−2i−2i−2i−2i2i2i2i2i-2-2-22200000000000002i−2i00000000
χ212222-1222-1222-122-1-12222-1-1-12-122-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-12-1-1-12-1-1-1000000002020022000000-10-100-1-1
χ222222-1222-1222-122-1-12222-1-1-12-122-1-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-12-1-1-12-1-1-100000000-20-200-2-20000001010011
χ232222-1222-122-2-1-22-1-12-2-22-1-1-12-122-1-1-1-1-1-1-21-111-21-1112-1-1-1-2111-21110000000020200-2-2000000-10-10011
χ242222-1222-122-2-1-22-1-12-2-22-1-1-12-122-1-1-1-1-1-1-21-111-21-1112-1-1-1-2111-211100000000-20-2002200000010100-1-1
χ252222-1222-1-2-22-122-1-1-2-2-22-1-1-12-1-2-21111112-1-1-1-12-1-1-1-1-2111-2111-21110000000020-2002-2000000-10100-11
χ262222-1222-1-2-22-122-1-1-2-2-22-1-1-12-1-2-21111112-1-1-1-12-1-1-1-1-2111-2111-211100000000-20200-2200000010-1001-1
χ272222-1222-1-2-2-2-1-22-1-1-2222-1-1-12-1-2-2111111-21-111-21-111-21112-1-1-12-1-1-10000000020-200-22000000-101001-1
χ282222-1222-1-2-2-2-1-22-1-1-2222-1-1-12-1-2-2111111-21-111-21-111-21112-1-1-12-1-1-100000000-202002-200000010-100-11
χ29222-1222-12222-12-12-1222-12-1-1-12-1-122-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-12-1-1-12-1-100000002020220000000-10-10-1-100
χ30222-1222-12222-12-12-1222-12-1-1-12-1-122-1-1-1-1-12-1-1-1-12-1-1-1-12-1-1-12-1-1-12-1-10000000-20-20-2-2000000010101100
χ31222-1222-1222-2-1-2-12-12-2-2-12-1-1-12-1-122-1-1-1-11-2-1111-2-111-12-1-11-2111-21100000002020-2-20000000-10-101100
χ32222-1222-1222-2-1-2-12-12-2-2-12-1-1-12-1-122-1-1-1-11-2-1111-2-111-12-1-11-2111-2110000000-20-202200000001010-1-100
χ33222-1222-12-2-22-12-12-1-2-2-2-12-1-1-1211-2-21111-12-1-1-1-12-1-1-11-2111-2111-211000000020-202-20000000-1010-1100
χ34222-1222-12-2-22-12-12-1-2-2-2-12-1-1-1211-2-21111-12-1-1-1-12-1-1-11-2111-2111-2110000000-2020-22000000010-101-100
χ35222-1222-12-2-2-2-1-2-12-1-222-12-1-1-1211-2-211111-2-1111-2-1111-211-12-1-1-12-1-1000000020-20-220000000-10101-100
χ36222-1222-12-2-2-2-1-2-12-1-222-12-1-1-1211-2-211111-2-1111-2-1111-211-12-1-1-12-1-10000000-20202-2000000010-10-1100
χ3722-2222-2220022-2-2-22000-2-2-2-2220000000022-222-2-22-2-200000000000022-22-200000000002-200000000000
χ3822-2222-2220022-2-2-22000-2-2-2-2220000000022-222-2-22-2-2000000000000-2-22-220000000000-2200000000000
χ3922-2222-22200-222-2-22000-2-2-2-22200000000-2-2-2-2-22222200000000000022-22-20000000000-2200000000000
χ4022-2222-22200-222-2-22000-2-2-2-22200000000-2-2-2-2-222222000000000000-2-22-2200000000002-200000000000
χ4122-222-222222020-2-22-2002222-2-22222222200-20000-200-2-2-2-20000000022-2-22220000000000-20000000000
χ4222-222-222222020-2-22-2002222-2-22222222200-20000-200-2-2-2-200000000-2-222-2-2-2000000000020000000000
χ4322-222-2222-2-2020-2-222002222-2-2-2-2-2-2-2-2-2-200-20000-20022220000000022-2-22-2-2000000000020000000000
χ4422-222-2222-2-2020-2-222002222-2-2-2-2-2-2-2-2-2-200-20000-200222200000000-2-222-2220000000000-20000000000
χ454444-2-4-44-2000-204-2-204i−4i-4222-420000000000-2000020000004i−2i−2i−2i−4i2i2i2i0000000000000000000000000000
χ464444-2-4-44-2000-204-2-20−4i4i-4222-420000000000-200002000000−4i2i2i2i4i−2i−2i−2i0000000000000000000000000000
χ47444-24-4-4-24000-20-24-204i−4i2-4222-40000000000-200002000000−2i4i−2i−2i2i−4i2i2i0000000000000000000000000000
χ48444-24-4-4-24000-20-24-20−4i4i2-4222-40000000000-2000020000002i−4i2i2i−2i4i−2i−2i0000000000000000000000000000
χ49444-2-244-2-244414-2-21444-2-211-2-2-2-2-2-21111-2-2111-2-2111-2-211-2-211-2-2110000000000000000000000000000
χ50444-2-244-2-244-41-4-2-214-4-4-2-211-2-2-2-2-2-21111221-1-1221-1-1-2-21122-1-122-1-10000000000000000000000000000
χ51444-2-244-2-2-4-4414-2-21-4-4-4-2-211-2-22222-1-1-1-1-2-2111-2-211122-1-122-1-122-1-10000000000000000000000000000
χ52444-2-244-2-2-4-4-41-4-2-21-444-2-211-2-22222-1-1-1-1221-1-1221-1-122-1-1-2-211-2-2110000000000000000000000000000
χ53444-2-2-4-4-2-200010-2-2104i−4i22-1-12200003i3i−3i−3i0013-300-13-3003i−3i−2i−2iii2i2i−i−i0000000000000000000000000000
χ54444-2-2-4-4-2-200010-2-2104i−4i22-1-1220000−3i−3i3i3i001-3300-1-3300−3i3i−2i−2iii2i2i−i−i0000000000000000000000000000
χ55444-2-2-4-4-2-200010-2-210−4i4i22-1-12200003i3i−3i−3i001-3300-1-33003i−3i2i2i−i−i−2i−2iii0000000000000000000000000000
χ56444-2-2-4-4-2-200010-2-210−4i4i22-1-1220000−3i−3i3i3i0013-300-13-300−3i3i2i2i−i−i−2i−2iii0000000000000000000000000000
χ5744-44-24-44-2004-2-4-42-2000-42224-2000000004-22-2-2-42-2220000000000000000000000000000000000000000
χ5844-44-24-44-200-4-24-42-2000-42224-200000000-422224-2-2-2-20000000000000000000000000000000000000000
χ5944-44-2-444-2440-20-42-2-4004-2-2-2-4244-2-2-2-2-2-20020000200-4222000000000000000000000000000000000000
χ6044-44-2-444-2-4-40-20-42-24004-2-2-2-42-4-422222200200002004-2-2-2000000000000000000000000000000000000
χ6144-4-244-4-24004-2-42-4-20002-422-2400000000-242-2-22-4-2220000000000000000000000000000000000000000
χ6244-4-244-4-2400-4-242-4-20002-422-24000000002-4222-24-2-2-20000000000000000000000000000000000000000
χ6344-4-24-44-24440-202-4-2-400-24-2-22-4-2-244-2-2-2-200200002002-422000000000000000000000000000000000000
χ6444-4-24-44-24-4-40-202-4-2400-24-2-22-422-4-422220020000200-24-2-2000000000000000000000000000000000000
χ6544-4-2-24-4-2-20041-422100022-1-1-2-200003i3i−3i−3i-2-2-111221-1-100−3i3i003i−3i003i−3i0000000000000000000000000000
χ6644-4-2-24-4-2-20041-422100022-1-1-2-20000−3i−3i3i3i-2-2-111221-1-1003i−3i00−3i3i00−3i3i0000000000000000000000000000
χ6744-4-2-24-4-2-200-41422100022-1-1-2-200003i3i−3i−3i22-1-1-1-2-211100−3i3i00−3i3i00−3i3i0000000000000000000000000000
χ6844-4-2-24-4-2-200-41422100022-1-1-2-20000−3i−3i3i3i22-1-1-1-2-2111003i−3i003i−3i003i−3i0000000000000000000000000000
χ6944-4-2-2-44-2-244010221-400-2-21122-2-2-2-2111100-13-300-1-3322-1-1003-300-330000000000000000000000000000
χ7044-4-2-2-44-2-244010221-400-2-21122-2-2-2-2111100-1-3300-13-322-1-100-33003-30000000000000000000000000000
χ7144-4-2-2-44-2-2-4-4010221400-2-211222222-1-1-1-100-13-300-1-33-2-21100-33003-30000000000000000000000000000
χ7244-4-2-2-44-2-2-4-4010221400-2-211222222-1-1-1-100-1-3300-13-3-2-211003-300-330000000000000000000000000000
χ734-404400-4-42i2−2i204000-40000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000004-40002i2−2i2000000000000000000000
χ744-404400-4-42i2−2i204000-40000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000-44000−2i22i2000000000000000000000
χ754-404400-4-4−2i22i204000-4000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000004-4000−2i22i2000000000000000000000
χ764-404400-4-4−2i22i204000-4000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000-440002i2−2i2000000000000000000000
χ778-808-400-844i2−4i20-400040000000004i2−4i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000000000
χ788-808-400-84−4i24i20-40004000000000−4i24i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000000000
χ798-80-48004-84i2−4i20-40004000000000−2i22i24i2−4i2−2i22i2−2i22i200000000000000000000000000000000000000000000000000
χ808-80-48004-8−4i24i20-400040000000002i2−2i2−4i24i22i2−2i22i2−2i200000000000000000000000000000000000000000000000000
χ818-80-4-400444i2−4i202000-2000006i−6i00−2i22i2−2i22i24ζ−2ζ3−4ζ+2ζ3−2ζ+4ζ32ζ−4ζ300000000000000000000000000000000000000000000000000
χ828-80-4-400444i2−4i202000-200000−6i6i00−2i22i2−2i22i2−2ζ+4ζ32ζ−4ζ34ζ−2ζ3−4ζ+2ζ300000000000000000000000000000000000000000000000000
χ838-80-4-40044−4i24i202000-2000006i−6i002i2−2i22i2−2i2−4ζ+2ζ34ζ−2ζ32ζ−4ζ3−2ζ+4ζ300000000000000000000000000000000000000000000000000
χ848-80-4-40044−4i24i202000-200000−6i6i002i2−2i22i2−2i22ζ−4ζ3−2ζ+4ζ3−4ζ+2ζ34ζ−2ζ300000000000000000000000000000000000000000000000000

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