Finite Group Databasebeta

← Group #11778589

Character table — Group #11778589

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222244444444444444444488888888888888888888888824242424242424242424242424242424363648484848727272
order12222233666666344666666666661212121244121212121212121212121212121212121212121212124444888824242424242424244412121212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-11-111-1-11111-1-1-1-1-1-11-11-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-11-11-1-111-1-1-1-11111-1-1-11-11-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-11-11-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-11-11-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1
χ9222222222222222-2-222222222222-2-2-2-20000000000-2-2-2-2-2-2000000000000000000000000220000-200
χ10222222222222222-2-222222222222-2-2-2-20000000000-2-2-2-2-2-2000000000000000000000000-2-20000200
χ112222222-12-12-12-1-12222-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1020200220000-1-1-1-1000-10-1000
χ122222222-12-12-12-1-12222-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-1-10-20-200-2-200001111000101000
χ132222222-12-12-12-1-12222-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-211112-1-1-1-1-111111111020200-2-200001111000-10-1000
χ142222222-12-12-12-1-12222-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-211112-1-1-1-1-1111111110-20-200220000-1-1-1-1000101000
χ15222222-12-12-12-12-122-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-12222-12-1-1-1-1-1-1-1-1-1-1-1-120202200-1-1-1-1000000-10-10000
χ16222222-12-12-12-12-122-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-12222-12-1-1-1-1-1-1-1-1-1-1-1-1-20-20-2-20011110000001010000
χ17222222-12-12-12-12-122-1-122-1-1-1-1-1-1-1-1-122-2-21111-2-2-2-2-12-1-1-1-1111111112020-2-2001111000000-10-10000
χ18222222-12-12-12-12-122-1-122-1-1-1-1-1-1-1-1-122-2-21111-2-2-2-2-12-1-1-1-111111111-20-202200-1-1-1-10000001010000
χ192222-2-22222222222-2-2-2-2-22-2-2-2-22222-2-20000000000-2222-2-20000000020-200000000000000020-20000
χ202222-2-22222222222-2-2-2-2-22-2-2-2-22222-2-20000000000-2222-2-200000000-202000000000000000-2020000
χ212222-2-2222222222-22-2-2-2-22-2-2-2-222-2-22200000000002-2-2-22200000000020-200000000000000020-2000
χ222222-2-2222222222-22-2-2-2-22-2-2-2-222-2-22200000000002-2-2-222000000000-202000000000000000-202000
χ232222-2-22-12-12-12-1-1-22-2-211-11111-1-1-2-2-1-1000000−i3−i3i3i32111-1-1−i3−i3−i3−i3i3i3i3i3020-200000000−i3−i3i3i3000-101000
χ242222-2-22-12-12-12-1-1-22-2-211-11111-1-1-2-2-1-1000000−i3−i3i3i32111-1-1−i3−i3−i3−i3i3i3i3i30-20200000000i3i3−i3−i300010-1000
χ252222-2-22-12-12-12-1-1-22-2-211-11111-1-1-2-2-1-1000000i3i3−i3−i32111-1-1i3i3i3i3−i3−i3−i3−i3020-200000000i3i3−i3−i3000-101000
χ262222-2-22-12-12-12-1-1-22-2-211-11111-1-1-2-2-1-1000000i3i3−i3−i32111-1-1i3i3i3i3−i3−i3−i3−i30-20200000000−i3−i3i3i300010-1000
χ272222-2-2-12-12-12-12-12-211-2-2-11111-1-1-1-1-2-200−i3−i3i3i3000012-1-111−i3−i3i3i3−i3−i3i3i320-200000−i3−i3i3i3000000-1010000
χ282222-2-2-12-12-12-12-12-211-2-2-11111-1-1-1-1-2-200−i3−i3i3i3000012-1-111−i3−i3i3i3−i3−i3i3i3-20200000i3i3−i3−i300000010-10000
χ292222-2-2-12-12-12-12-12-211-2-2-11111-1-1-1-1-2-200i3i3−i3−i3000012-1-111i3i3−i3−i3i3i3−i3−i320-200000i3i3−i3−i3000000-1010000
χ302222-2-2-12-12-12-12-12-211-2-2-11111-1-1-1-1-2-200i3i3−i3−i3000012-1-111i3i3−i3−i3i3i3−i3−i3-20200000−i3−i3i3i300000010-10000
χ312-22-2-222222-2-2-2-22002-22-2-222-2-2-2200000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-20000000
χ322-22-2-222222-2-2-2-22002-22-2-222-2-2-2200000000000000000000000000000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2-220000000
χ332-22-2-222222-2-2-2-22002-22-2-222-2-2-2200000000000000000000000000000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2-220000000
χ342-22-2-222222-2-2-2-22002-22-2-222-2-2-2200000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-20000000
χ354444444-24-24-24-2-2-4-444-2-2-2-2-2-2-2-2-2-4-4220000000000-422222000000000000000000000000000000000
χ36444444-24-24-24-24-2-4-4-2-244-2-2-2-2-2-2-222-4-400000000002-42222000000000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2144-2-2-2-21111111-2-2-2-244-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2144-2-2-2-21111111-2-2-2-2-4-422222222-2-21111-1-1-1-1-1-1-1-10000000000000000000000000
χ39444444-2-2-2-2-2-2-2-21-4-4-2-2-2-211111112222000000000022-1-1-1-133-3-3-3-3330000000000000000000000000
χ40444444-2-2-2-2-2-2-2-21-4-4-2-2-2-211111112222000000000022-1-1-1-1-3-33333-3-30000000000000000000000000
χ414444-4-44-24-24-24-2-24-4-4-422-22222-2-244220000000000-4-2-2-222000000000000000000000000000000000
χ424444-4-4-24-24-24-24-2-4422-4-4-22222-2-222440000000000-2-422-2-2000000000000000000000000000000000
χ434444-4-4-2-2-2-2-2-2-2-214-422221-1-1-1-111-2-22200−2i3−2i32i32i300002-211-1-1i3i3−i3−i3i3i3−i3−i30000000000000000000000000
χ444444-4-4-2-2-2-2-2-2-2-214-422221-1-1-1-111-2-222002i32i3−2i3−2i300002-211-1-1−i3−i3i3i3−i3−i3i3i30000000000000000000000000
χ454444-4-4-2-2-2-2-2-2-2-21-4422221-1-1-1-11122-2-2000000−2i3−2i32i32i3-22-1-111i3i3i3i3−i3−i3−i3−i30000000000000000000000000
χ464444-4-4-2-2-2-2-2-2-2-21-4422221-1-1-1-11122-2-20000002i32i3−2i3−2i3-22-1-111−i3−i3−i3−i3i3i3i3i30000000000000000000000000
χ4744-4-40044-4-444-4-4400000040000-4-40000000000000000000000000000000000000000000000000002-2
χ4844-4-40044-4-444-4-4400000040000-4-4000000000000000000000000000000000000000000000000000-22
χ494-44-44-44444-4-4-4-4400-44-44-4-4-444-4400000000000000000000000000000000000000000000000000000
χ504-44-44-44-24-2-42-42-200-442-2222-2-22-200000000000000000000000000000000000000006−6−66000000000
χ514-44-44-44-24-2-42-42-200-442-2222-2-22-20000000000000000000000000000000000000000−666−6000000000
χ524-44-44-4-24-242-42-4-2002-2-44222-2-22-20000000000000000000000000000000000006−6−660000000000000
χ534-44-44-4-24-242-42-4-2002-2-44222-2-22-2000000000000000000000000000000000000−666−60000000000000
χ544-44-4-444-24-2-42-42-2004-4-222-2-2222-20000000000000000000000000000000000−2i22i20000i2−i2i2−i2000000000
χ554-44-4-444-24-2-42-42-2004-4-222-2-2222-200000000000000000000000000000000002i2−2i20000−i2i2−i2i2000000000
χ564-44-4-44-24-242-42-4-200-224-42-2-2222-200000000000000000000000000000000−2i22i200i2−i2i2−i20000000000000
χ574-44-4-44-24-242-42-4-200-224-42-2-2222-2000000000000000000000000000000002i2−2i200−i2i2−i2i20000000000000
χ584-4-440044-4-4-4-4444000000-400004-400002i−2i2i−2i2i−2i2i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000
χ594-4-440044-4-4-4-4444000000-400004-40000−2i2i−2i2i−2i2i−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000
χ604-4-44004-2-42-424-2-200000020000-2200−2i32i32i−2i2i−2i2i−2i2ζ14−2ζ142ζ22−2ζ220000−2i32i32ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ220000000000000000000000000
χ614-4-44004-2-42-424-2-200000020000-2200−2i32i3−2i2i−2i2i−2i2i−2ζ142ζ14−2ζ222ζ220000−2i32i3−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ220000000000000000000000000
χ624-4-44004-2-42-424-2-200000020000-22002i3−2i32i−2i2i−2i2i−2i2ζ22−2ζ222ζ14−2ζ1400002i3−2i32ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ140000000000000000000000000
χ634-4-44004-2-42-424-2-200000020000-22002i3−2i3−2i2i−2i2i−2i2i−2ζ222ζ22−2ζ142ζ1400002i3−2i3−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ140000000000000000000000000
χ644-4-4400-242-42-4-24-200000020000-22−2i32i3002i−2i2ζ14−2ζ142ζ22−2ζ222i−2i2i−2i00−2i32i3002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000
χ654-4-4400-242-42-4-24-200000020000-22−2i32i300−2i2i−2ζ142ζ14−2ζ222ζ22−2i2i−2i2i00−2i32i300−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000
χ664-4-4400-242-42-4-24-200000020000-222i3−2i3002i−2i2ζ22−2ζ222ζ14−2ζ142i−2i2i−2i002i3−2i3002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000
χ674-4-4400-242-42-4-24-200000020000-222i3−2i300−2i2i−2ζ222ζ22−2ζ142ζ14−2i2i−2i2i002i3−2i300−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000
χ684-4-4400-2-22222-2-21000000-13-33-31-1−2i32i3−2i32i32i−2i2ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200i3−i3i3−i3−3ζ14−ζ223ζ14+ζ22−ii−ii−ζ14−3ζ22ζ14+3ζ220000000000000000000000000
χ694-4-4400-2-22222-2-21000000-13-33-31-1−2i32i3−2i32i3−2i2i−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200i3−i3i3−i33ζ14+ζ22−3ζ14−ζ22i−ii−iζ14+3ζ22−ζ14−3ζ220000000000000000000000000
χ704-4-4400-2-22222-2-21000000-13-33-31-12i3−2i32i3−2i32i−2i2ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400−i3i3−i3i3−ζ14−3ζ22ζ14+3ζ22−ii−ii−3ζ14−ζ223ζ14+ζ220000000000000000000000000
χ714-4-4400-2-22222-2-21000000-13-33-31-12i3−2i32i3−2i3−2i2i−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400−i3i3−i3i3ζ14+3ζ22−ζ14−3ζ22i−ii−i3ζ14+ζ22−3ζ14−ζ220000000000000000000000000
χ724-4-4400-2-22222-2-21000000-1-33-331-1−2i32i32i3−2i32i−2i2ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ1400i3−i3−i3i3−ii−ζ14−3ζ22ζ14+3ζ22−3ζ14−ζ223ζ14+ζ22−ii0000000000000000000000000
χ734-4-4400-2-22222-2-21000000-1-33-331-1−2i32i32i3−2i3−2i2i−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ1400i3−i3−i3i3i−iζ14+3ζ22−ζ14−3ζ223ζ14+ζ22−3ζ14−ζ22i−i0000000000000000000000000
χ744-4-4400-2-22222-2-21000000-1-33-331-12i3−2i3−2i32i32i−2i2ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ2200−i3i3i3−i3−ii−3ζ14−ζ223ζ14+ζ22−ζ14−3ζ22ζ14+3ζ22−ii0000000000000000000000000
χ754-4-4400-2-22222-2-21000000-1-33-331-12i3−2i3−2i32i3−2i2i−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ2200−i3i3i3−i3i−i3ζ14+ζ22−3ζ14−ζ22ζ14+3ζ22−ζ14−3ζ22i−i0000000000000000000000000
χ7688-8-8008-4-848-4-84-4000000-400004400000000000000000000000000000000000000000000000000000
χ7788-8-800-484-8-484-8-4000000-400004400000000000000000000000000000000000000000000000000000
χ7888-8-800-4-444-4-444200000026-6-66-2-200000000000000000000000000000000000000000000000000000
χ7988-8-800-4-444-4-44420000002-666-6-2-200000000000000000000000000000000000000000000000000000
χ808-88-88-8-4-4-4-444442004-44-4-2-2-222-2200000000000000000000000000000000000000000000000000000
χ818-88-8-88-4-4-4-44444200-44-44-222-2-2-2200000000000000000000000000000000000000000000000000000

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