Finite Group Databasebeta

← Group #13151332

Character table — Group #13151332

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order12223446662212123366666666222236666666121212124444444444666666666612122222226666121212121212121212126666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111-1-11111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ61111111111-1-11111111111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111-1-11111111111-1-1-1-1-1-11-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111
χ81111111111-1-11111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-111-1-1
χ911111-1-11111-1-1-1111111111-11111111-1-1111-1-1-1-1-1-111-1-111-1-111111-111-1-1-1-11-11-11-111-1-111-1-111-1-1-1-11-11-1
χ1011111-1-11111-1-1-1111111111-11111111-1-1111-1-1-1-1-1-1-1-111-1-11111111-111-1-1-1-11-1-11-1111-1-1-1-111-1-111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-111-1-1-1-11-111-1-1-1-1-111-1-11-1-11111-1-1-1-111111-1-11
χ1211111-1-11111-1-1-1111111111-1-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-11-111-1-1-1-1-11-111-1-1-111-1-11111-1-111-111-1
χ1311111-1-1111-11-1-111111111-1111111-1-111111-1-1-1-1-1-111-1-111-1-11111-11-1-111-1-1-11-11-11-1-11111-1-111-1-1-1-1-11-11
χ1411111-1-1111-11-1-111111111-1111111-1-111111-1-1-1-1-1-1-1-111-1-1111111-11-1-111-1-1-111-11-1-1-111-1-111-1-111-1-11-11-1
χ1511111-1-1111-11-1-111111111-11-1-1-1-11-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-111-1-11-1-111-111-1-111-1-1-1-11111-111-1
χ1611111-1-1111-11-1-111111111-11-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-111-1-11-11-1-1111-1-1-1-11111-1-1111-1-11
χ17222222222222222-1-1-1222-1222222-1-1-1-1-1-1-1-122-1-12200000000-1-1-1-122-1-1-1-1-1-1220000-1-1-1-100000000-1-10000
χ18222222222222222-1-1-1222-122-2-2-2-2-1-1-1-1-1-1-1-122-1-1-2-200000000111122-1-1-1-1-1-1-2-20000111100000000110000
χ1922222222222222-1222-1-1-12220000-12222-1-1-1-1-12200000022220000-1-1-1-1-1-1-1-100002200000000-1-1-1-10000-1-1
χ2022222222222222-1222-1-1-12220000-12222-1-1-1-1-122000000-2-2-2-20000-1-1-1-1-1-1-1-10000-2-2000000001111000011
χ212222222222-2-2222-1-1-1222-1-2-22222-11111-1-1-122-1-12200000000-1-1-1-1-2-21111-1-1-2-20000111100000000-1-10000
χ222222222222-2-2222-1-1-1222-1-2-2-2-2-2-2-11111-1-1-122-1-1-2-2000000001111-2-21111-1-1220000-1-1-1-100000000110000
χ232222222222-2-222-1222-1-1-12-2-20000-1-2-2-2-2-1-1-1-1-12200000022220000111111-1-10000-2-200000000-1-1-1-1000011
χ242222222222-2-222-1222-1-1-12-2-20000-1-2-2-2-2-1-1-1-1-122000000-2-2-2-20000111111-1-10000220000000011110000-1-1
χ2522222-2-22222-2-2-22-1-1-1222-12-22222-1-1-111-1-1-1-2-211-2-200000000-1-1-1-12-2-1-111112-20000-1-11100000000110000
χ2622222-2-22222-2-2-22-1-1-1222-12-2-2-2-2-2-1-1-111-1-1-1-2-211220000000011112-2-1-11111-22000011-1-100000000-1-10000
χ2722222-2-22222-2-2-2-1222-1-1-122-20000-122-2-2-1-1-111-2-200000022-2-20000-11-1-1111100002-200000000-1-1110000-11
χ2822222-2-22222-2-2-2-1222-1-1-122-20000-122-2-2-1-1-111-2-2000000-2-2220000-11-1-111110000-220000000011-1-100001-1
χ2922222-2-2222-22-2-22-1-1-1222-1-222222-111-1-1-1-1-1-2-211-2-200000000-1-1-1-1-2211-1-111-22000011-1-100000000110000
χ3022222-2-2222-22-2-22-1-1-1222-1-22-2-2-2-2-111-1-1-1-1-1-2-21122000000001111-2211-1-1112-20000-1-11100000000-1-10000
χ3122222-2-2222-22-2-2-1222-1-1-12-220000-1-2-222-1-1-111-2-200000022-2-200001-111-1-1110000-2200000000-1-11100001-1
χ3222222-2-2222-22-2-2-1222-1-1-12-220000-1-2-222-1-1-111-2-2000000-2-22200001-111-1-11100002-20000000011-1-10000-11
χ3322-2-222-22-2-2002-222-2-22-2-220022-2-220000-2-222-22-22-20000000022-2-20000002-20000000000000000002-20000
χ3422-2-222-22-2-2002-222-2-22-2-2200-2-22220000-2-222-22-2-2200000000-2-2220000002-2000000000000000000-220000
χ3522-2-222-22-2-2002-22-1112-2-2-10022-2-2-1i3−i3i3−i311-12-2-112-200000000-1-11100i3−i3i3−i3-11000000i3−i3i3−i300000000-110000
χ3622-2-222-22-2-2002-22-1112-2-2-10022-2-2-1−i3i3−i3i311-12-2-112-200000000-1-11100−i3i3−i3i3-11000000−i3i3−i3i300000000-110000
χ3722-2-222-22-2-2002-22-1112-2-2-100-2-222-1i3−i3i3−i311-12-2-11-220000000011-1-100i3−i3i3−i3-11000000−i3i3−i3i3000000001-10000
χ3822-2-222-22-2-2002-22-1112-2-2-100-2-222-1−i3i3−i3i311-12-2-11-220000000011-1-100−i3i3−i3i3-11000000i3−i3i3−i3000000001-10000
χ3922-2-22-222-2-200-2222-2-22-2-220022-2-220000-2-22-22-22-220000000022-2-2000000-22000000000000000000-220000
χ4022-2-22-222-2-200-2222-2-22-2-2200-2-22220000-2-22-22-222-200000000-2-222000000-220000000000000000002-20000
χ4122-2-22-222-2-200-222-1112-2-2-10022-2-2-1i3−i3−i3i311-1-221-1-2200000000-1-11100i3−i3−i3i31-1000000i3−i3−i3i3000000001-10000
χ4222-2-22-222-2-200-222-1112-2-2-10022-2-2-1−i3i3i3−i311-1-221-1-2200000000-1-11100−i3i3i3−i31-1000000−i3i3i3−i3000000001-10000
χ4322-2-22-222-2-200-222-1112-2-2-100-2-222-1i3−i3−i3i311-1-221-12-20000000011-1-100i3−i3−i3i31-1000000−i3i3i3−i300000000-110000
χ4422-2-22-222-2-200-222-1112-2-2-100-2-222-1−i3i3i3−i311-1-221-12-20000000011-1-100−i3i3i3−i31-1000000i3−i3−i3i300000000-110000
χ452-22-2200-22-20000222-2-22-2-2002-22-2200002-2-2000000002-2002-22-22-2000000000000000000002-2002-2000000
χ462-22-2200-22-20000222-2-22-2-2002-22-2200002-2-200000000-2200-222-22-200000000000000000000-2200-22000000
χ472-22-2200-22-20000222-2-22-2-200-22-22200002-2-2000000002-200-22-22-22000000000000000000002-200-22000000
χ482-22-2200-22-20000222-2-22-2-200-22-22200002-2-200000000-22002-2-22-2200000000000000000000-22002-2000000
χ492-2-22200-2-22000022-22-2-22-2002-2-2220000-22-20000002-2002-2002-2-220000000000000000002-2002-200000000
χ502-2-22200-2-22000022-22-2-22-2002-2-2220000-22-2000000-2200-22002-2-22000000000000000000-2200-2200000000
χ512-2-22200-2-22000022-22-2-22-200-222-220000-22-20000002-200-2200-222-20000000000000000002-200-2200000000
χ522-2-22200-2-22000022-22-2-22-200-222-220000-22-2000000-22002-200-222-2000000000000000000-22002-200000000
χ5344444444444444-2-2-2-2-2-2-2-24400001-2-2-2-2111-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-4000012222111-2-2-2-20000000000000022-1-1-1-111000000000000000000000000
χ5544444-4-44444-4-4-4-2-2-2-2-2-2-2-24-400001-2-222111222200000000000000-2211-1-1-1-1000000000000000000000000
χ5644444-4-4444-44-4-4-2-2-2-2-2-2-2-2-440000122-2-21112222000000000000002-2-1-111-1-1000000000000000000000000
χ5744-4-444-44-4-4004-4-24-4-4-2224000000-2000022-2-224-400000000000000000000-22000000000000000000000000
χ5844-4-444-44-4-4004-4-2-222-222-200000012i3−2i32i3−2i3-1-11-22-220000000000000000−i3i3−i3i31-1000000000000000000000000
χ5944-4-444-44-4-4004-4-2-222-222-20000001−2i32i3−2i32i3-1-11-22-220000000000000000i3−i3i3−i31-1000000000000000000000000
χ6044-4-44-444-4-400-44-24-4-4-2224000000-2000022-22-2-44000000000000000000002-2000000000000000000000000
χ6144-4-44-444-4-400-44-2-222-222-200000012i3−2i3−2i32i3-1-112-22-20000000000000000−i3i3i3−i3-11000000000000000000000000
χ6244-4-44-444-4-400-44-2-222-222-20000001−2i32i32i3−2i3-1-112-22-20000000000000000i3−i3−i3i3-11000000000000000000000000
χ634-44-4400-44-400004-2-22-44-42004-44-4-20000-22200000000000000-22-2200000000000000000000000000000000
χ644-44-4400-44-400004-2-22-44-4200-44-44-20000-222000000000000002-22-200000000000000000000000000000000
χ654-44-4400-44-40000-244-42-22-4000000-20000-2220000000000004-40000000000000000000000000000-22000000
χ664-44-4400-44-40000-244-42-22-4000000-20000-222000000000000-4400000000000000000000000000002-2000000
χ674-4-44400-4-4400004-22-2-4-442004-4-44-200002-2200000000000000-222-200000000000000000000000000000000
χ684-4-44400-4-4400004-22-2-4-44200-444-4-200002-22000000000000002-2-2200000000000000000000000000000000
χ694-4-44400-4-440000-24-4422-2-4000000-200002-2200000000004-40000000000000000000000000000-2200000000
χ704-4-44400-4-440000-24-4422-2-4000000-200002-220000000000-4400000000000000000000000000002-200000000
χ716666-366-3-3-366-3-300000000-3-3000000000000000000222200000000000000000022000000-1-1-1-1000000-1-100
χ726666-366-3-3-366-3-300000000-3-3000000000000000000-2-2-2-2000000000000000000-2-200000011110000001100
χ736666-366-3-3-3-6-6-3-300000000330000000000000000002222000000000000000000-2-2000000-1-1-1-10000001100
χ746666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2-2-2000000000000000000220000001111000000-1-100
χ756666-3-6-6-3-3-36-63300000000-3300000000000000000022-2-20000000000000000002-2000000-1-111000000-1100
χ766666-3-6-6-3-3-36-63300000000-33000000000000000000-2-222000000000000000000-2200000011-1-10000001-100
χ776666-3-6-6-3-3-3-6633000000003-300000000000000000022-2-2000000000000000000-22000000-1-1110000001-100
χ786666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-2220000000000000000002-200000011-1-1000000-1100
χ798-88-8800-88-80000-4-4-444-444000000200002-2-200000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-44-444-4400000020000-22-200000000000000000000000000000000000000000000000000
χ811212-12-12-612-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-1212-666006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6006-6600000000000000000000000000000000004-40000000000000000000000000000-220000000000
χ8412-1212-12-6006-660000000000000000000000000000000000-4400000000000000000000000000002-20000000000
χ8512-12-1212-60066-6000000000000000000000000000000004-40000000000000000000000000000-22000000000000
χ8612-12-1212-60066-600000000000000000000000000000000-4400000000000000000000000000002-2000000000000

Here i is the imaginary unit (i² = −1).