Finite Group Databasebeta

← Group #11778786

Character table — Group #11778786

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222244444444444488888888888888812121212121216161616161624242424242424242424242424242424242424242472727272
order122222336666663446666666121224666612121212121212121244121212126661212122444466881212121212121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1111-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-111-1-1-111-1-11111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-111111111-1-1
χ9222222222222222-2-22222222-2-2000022-2-2-200-2-2-2-22222220000000-20000000-2-200000000000000
χ10222222222222222-2-22222222-2-2000022-2-2-200-2-2-2-2-2-2-2-2-2-20000000200000002200000000000000
χ112222222-1-122-12-1-12222-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12-1-12-1-122002-1-100-1-10000-1-100000000
χ122222222-1-122-12-1-12222-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-1-2-211112-1-12-1-1-2-200-211001100001100000000
χ132222222-1-122-12-1-12222-1-1-1-1-122-2-211-1-12-1-111-1-1-1-122-1-1-1-1-211-211-2200-21100-1-100001100000000
χ142222222-1-122-12-1-12222-1-1-1-1-122-2-211-1-12-1-111-1-1-1-1-2-21111-211-2112-2002-1-100110000-1-100000000
χ152222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200−i3i3-1-1-211−i3i3111122-1-1-1-10−i3i30−i3i30-2000−i3i300110000−i3i300000000
χ162222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200−i3i3-1-1-211−i3i31111-2-211110−i3i30−i3i302000i3−i300-1-10000i3−i300000000
χ172222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200i3−i3-1-1-211i3−i3111122-1-1-1-10i3−i30i3−i30-2000i3−i300110000i3−i300000000
χ182222222-1-122-12-1-1-2-222-1-1-1-1-1-2-200i3−i3-1-1-211i3−i31111-2-211110i3−i30i3−i302000−i3i300-1-10000−i3i300000000
χ19222222-122-1-12-12-122-1-122-1-1-1-1-12222-1-1-12222-1-1-1-1000000-1-1-1-1-1-100220002200-1-1-1-100-1-1-1-10000
χ20222222-122-1-12-12-122-1-122-1-1-1-1-12222-1-1-12222-1-1-1-1000000-1-1-1-1-1-100-2-2000-2-20011110011110000
χ21222222-122-1-12-12-122-1-122-1-1-1-1-1-2-2-2-2-1-1-122-2-2-1-1-1-10000001111110022000-2-200-1-1-1-10011110000
χ22222222-122-1-12-12-122-1-122-1-1-1-1-1-2-2-2-2-1-1-122-2-2-1-1-1-100000011111100-2-20002200111100-1-1-1-10000
χ232222-2-22222222222-2-2-2-2-2222222-222-2-2-22-2-2-222-2-2000000222-2-2-20000000000000000000000000
χ242222-2-22222222222-2-2-2-2-222222-22-2-2-2-2-22-22222-2-2000000-2-2-22220000000000000000000000000
χ252222-2-2222222222-22-2-2-2-2222-2-20000-2-22-2200-2-2220000000000002000-22200000000-2-200000000
χ262222-2-2222222222-22-2-2-2-2222-2-20000-2-22-2200-2-222000000000000-20002-2-2000000002200000000
χ272222-2-22-1-122-12-1-12-2-2-211-1-1-1222-2-1-111-2-1111-1-11100−i3−i3i3i32-1-1-21100000−i3i300−i3i30000i3−i300000000
χ282222-2-22-1-122-12-1-12-2-2-211-1-1-1222-2-1-111-2-1111-1-11100i3i3−i3−i32-1-1-21100000i3−i300i3−i30000−i3i300000000
χ292222-2-22-1-122-12-1-12-2-2-211-1-1-122-221111-2-11-1-1-1-11100−i3−i3i3i3-2112-1-100000i3−i300−i3i30000−i3i300000000
χ302222-2-22-1-122-12-1-12-2-2-211-1-1-122-221111-2-11-1-1-1-11100i3i3−i3−i3-2112-1-100000−i3i300i3−i30000i3−i300000000
χ312222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-200−i3i31121-1i3−i311-1-100−i3−i3i3i30−i3i30i3−i32000-2-1-100i3−i300001100000000
χ322222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-200−i3i31121-1i3−i311-1-100i3i3−i3−i30−i3i30i3−i3-200021100−i3i30000-1-100000000
χ332222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-200i3−i31121-1−i3i311-1-100−i3−i3i3i30i3−i30−i3i3-200021100i3−i30000-1-100000000
χ342222-2-22-1-122-12-1-1-22-2-211-1-1-1-2-200i3−i31121-1−i3i311-1-100i3i3−i3−i30i3−i30−i3i32000-2-1-100−i3i300001100000000
χ352222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-12-2221112-2-2-2-1-111000000-1-1-111100000000000−i3−i3i3i300−i3−i3i3i30000
χ362222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-12-2221112-2-2-2-1-111000000-1-1-111100000000000i3i3−i3−i300i3i3−i3−i30000
χ372222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-1-22-2-21112-222-1-111000000111-1-1-100000000000−i3−i3i3i300i3i3−i3−i30000
χ382222-2-2-122-1-12-12-12-211-2-2-1-1-1-1-1-22-2-21112-222-1-111000000111-1-1-100000000000i3i3−i3−i300−i3−i3i3i30000
χ392-2-222-222-22-2-2-222002-22-2-22-20000002-20000000002-22-22-20000000000000−i2i200000000−i2i2−i2i200−i2i2
χ402-2-222-222-22-2-2-222002-22-2-22-20000002-20000000002-22-22-20000000000000i2−i200000000i2−i2i2−i200i2−i2
χ412-2-222-222-22-2-2-222002-22-2-22-20000002-2000000000-22-22-220000000000000−i2i200000000−i2i2−i2i200i2−i2
χ422-2-222-222-22-2-2-222002-22-2-22-20000002-2000000000-22-22-220000000000000i2−i200000000i2−i2i2−i200−i2i2
χ43444444-244-2-24-24-2-4-4-2-244-2-2-2220000-2-22-4-40022220000000000000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2144-2-2-2-2111-2-244-2-211-2-2-2-2-21111000000-211-2110000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2144-2-2-2-2111-2-2-4-42211-2-2-22211110000002-1-12-1-10000000000000000000000000
χ46444444-2-2-2-2-2-2-2-21-4-4-2-2-2-21112200−2i32i311222−2i32i3-1-1-1-10000000i3−i30i3−i30000000000000000000000000
χ47444444-2-2-2-2-2-2-2-21-4-4-2-2-2-211122002i3−2i3112222i3−2i3-1-1-1-10000000−i3i30−i3i30000000000000000000000000
χ484444-4-4-244-2-24-24-2-4422-4-4-2-2-222000022-2-440022-2-20000000000000000000000000000000000000
χ494444-4-4-2-2-2-2-2-2-2-214-42222111-2-24-4-2-2-1-12-222211-1-1000000-2112-1-10000000000000000000000000
χ504444-4-4-2-2-2-2-2-2-2-214-42222111-2-2-4422-1-12-22-2-211-1-10000002-1-1-2110000000000000000000000000
χ514444-4-4-2-2-2-2-2-2-2-21-4422221112200−2i32i3-1-1-22-22i3−2i3-1-1110000000i3−i30−i3i30000000000000000000000000
χ524444-4-4-2-2-2-2-2-2-2-21-44222211122002i3−2i3-1-1-22-2−2i32i3-1-1110000000−i3i30i3−i30000000000000000000000000
χ5344-4-40044-4-444-4-44000000-4-4400000000000000000000000000000002i−2i00000002i−2i2i−2i0000000000
χ5444-4-40044-4-444-4-44000000-4-440000000000000000000000000000000−2i2i0000000−2i2i−2i2i0000000000
χ5544-4-400-24-42-242-4-200000022-2−2i32i300000000000−2i32i300000000000000002i−2i00000002ζ14−2ζ142ζ22−2ζ220000000000
χ5644-4-400-24-42-242-4-200000022-2−2i32i300000000000−2i32i30000000000000000−2i2i0000000−2ζ142ζ14−2ζ222ζ220000000000
χ5744-4-400-24-42-242-4-200000022-22i3−2i3000000000002i3−2i300000000000000002i−2i00000002ζ22−2ζ222ζ14−2ζ140000000000
χ5844-4-400-24-42-242-4-200000022-22i3−2i3000000000002i3−2i30000000000000000−2i2i0000000−2ζ222ζ22−2ζ142ζ140000000000
χ594-44-400444-4-4-44-440000004-4-4000000000000000000000000000000000000000000000000002i−2i00
χ604-44-400444-4-4-44-440000004-4-400000000000000000000000000000000000000000000000000−2i2i00
χ614-4-444-44-224-42-4-2-2004-4-222-22000000-220000000004-4-22-220000000000000000000000000000000
χ624-4-444-44-224-42-4-2-2004-4-222-22000000-22000000000-442-22-20000000000000000000000000000000
χ634-4-444-4-24-4-22-424-200-224-42-22000000-220000000000000000000000000000−2i22i200000000i2−i2i2−i20000
χ644-4-444-4-24-4-22-424-200-224-42-22000000-2200000000000000000000000000002i2−2i200000000−i2i2−i2i20000
χ654-4-44-4444-44-4-4-44400-44-44-44-4000000-440000000000000000000000000000000000000000000000
χ664-4-44-444-224-42-4-2-200-442-22-220000002-200000000000−2i32i32i3−2i30000000000000000000000000000000
χ674-4-44-444-224-42-4-2-200-442-22-220000002-2000000000002i3−2i3−2i32i30000000000000000000000000000000
χ684-4-44-44-24-4-22-424-2002-2-442-220000002-2000000000000000000000000000000000000006−6−660000
χ694-4-44-44-24-4-22-424-2002-2-442-220000002-200000000000000000000000000000000000000−666−60000
χ7088-8-8008-44-88-4-84-400000044-4000000000000000000000000000000000000000000000000000000
χ7188-8-800-4-444-4-4442000000-2-22−4i34i3000000000002i3−2i3000000000000000000000000000000000000000
χ7288-8-800-4-444-4-4442000000-2-224i3−4i300000000000−2i32i3000000000000000000000000000000000000000
χ738-88-8008-4-4-8-8484-4000000-444000000000000000000000000000000000000000000000000000000
χ748-88-800-48844-8-4-8-4000000-444000000000000000000000000000000000000000000000000000000
χ758-88-800-4-4-4444-4420000002-2-20000000000000006i−6i0000000000000000000000000000000000000
χ768-88-800-4-4-4444-4420000002-2-2000000000000000−6i6i0000000000000000000000000000000000000
χ778-8-888-8-4-44-4444-4200-44-44-22-20000002-20000000000000000000000000000000000000000000000
χ788-8-88-88-4-44-4444-42004-44-4-22-2000000-220000000000000000000000000000000000000000000000

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