Finite Group Databasebeta

← Group #13151465

Character table — Group #13151465

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order12223446662212123366666666366666661212121222222222446666666666121222444446666661212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ51111111111-1-11111111111-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111111111-1-1-1-1-1-111-1-1
χ61111111111-1-11111111111-1-11-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-11111-1-11111-1-1-1-111
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1-111-1-1-1-111111111-1-1-1-1
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-11-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ911111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111111111111-111-1-1-1-11-1-1-1-11-11111-1-1-1-111-1-1-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-1-111-11-11-1-111-1-111-1-111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-1-1-1-1-1111-11-111-1-111-1-1-1-11111-111-1
χ1211111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-11-111-1-1-1-11-1-111-11-1-1-1-1111111-1-1111-1-11
χ1311111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-111-1-11-111-1-111111-1-1-1-1-1-111111-1-11
χ1411111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1-11-1111-1-1-111-1-11111-1-111-111-1
χ1511111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-1111111111111-11-1-111-1-1-11-1-1-1-1111-1-111-1-111-1-1-1-1-11-11
χ1611111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-11-11-111-1-1-1-1-11111-1-111-1-11-11-1
χ17222222222222222-1-1-1222-122-1-1-1-1-1-1-1-122-1-12222220000-1-1-1-122-1-1-1-1-1-1000200000-1-1-1-1000000-1-10000
χ18222222222222222-1-1-1222-122-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-20000111122-1-1-1-1-1-1000-2000001111000000110000
χ1922222222222222-1222-1-1-1222-12222-1-1-1-1-12200000000220000-1-1-1-1-1-1-1-1222000000000000-1-1-1-100-1-100
χ2022222222222222-1222-1-1-1222-12222-1-1-1-1-12200000000-2-20000-1-1-1-1-1-1-1-1-2-2-20000000000001111001100
χ212222222222-2-2222-1-1-1222-1-2-2-11111-1-1-122-1-12222-2-200001111-2-21111-1-1000-200000-1-1-1-1000000110000
χ222222222222-2-2222-1-1-1222-1-2-2-11111-1-1-122-1-1-2-2-2-2220000-1-1-1-1-2-21111-1-10002000001111000000-1-10000
χ232222222222-2-222-1222-1-1-12-2-2-1-2-2-2-2-1-1-1-1-12200000000220000111111-1-1-2-22000000000000-1-1-1-1001100
χ242222222222-2-222-1222-1-1-12-2-2-1-2-2-2-2-1-1-1-1-12200000000-2-20000111111-1-122-2000000000000111100-1-100
χ2522222-2-22222-2-2-22-1-1-1222-12-2-1-1-111-1-1-1-2-21122-2-2220000-1-1-1-12-2-1-11111000-200000-1-111000000110000
χ2622222-2-22222-2-2-22-1-1-1222-12-2-1-1-111-1-1-1-2-211-2-222-2-2000011112-2-1-1111100020000011-1-1000000-1-10000
χ2722222-2-22222-2-2-2-1222-1-1-122-2-122-2-2-1-1-111-2-200000000220000-11-1-111112-2-2000000000000-1-11100-1100
χ2822222-2-22222-2-2-2-1222-1-1-122-2-122-2-2-1-1-111-2-200000000-2-20000-11-1-11111-22200000000000011-1-1001-100
χ2922222-2-2222-22-2-22-1-1-1222-1-22-111-1-1-1-1-1-2-21122-2-2-2-200001111-2211-1-111000200000-1-111000000-1-10000
χ3022222-2-2222-22-2-22-1-1-1222-1-22-111-1-1-1-1-1-2-211-2-222220000-1-1-1-1-2211-1-111000-20000011-1-1000000110000
χ3122222-2-2222-22-2-2-1222-1-1-12-22-1-2-222-1-1-111-2-2000000002200001-111-1-111-22-2000000000000-1-111001-100
χ3222222-2-2222-22-2-2-1222-1-1-12-22-1-2-222-1-1-111-2-200000000-2-200001-111-1-1112-2200000000000011-1-100-1100
χ332-22-222-2-22-2002-222-2-22-2-220020000-2-222-22-22-22-200000000000000002-20000000002-22-2000000000000
χ342-22-222-2-22-2002-222-2-22-2-220020000-2-222-22-2-22-2200000000000000002-2000000000-22-22000000000000
χ352-22-222-2-22-2002-22-1112-2-2-100-1−i3i3−i3i311-12-2-112-22-2000000−i3−i3i3i300−i3i3−i3i3-11000000000-11-11000000−i3i30000
χ362-22-222-2-22-2002-22-1112-2-2-100-1−i3i3−i3i311-12-2-11-22-22000000i3i3−i3−i300−i3i3−i3i3-110000000001-11-1000000i3−i30000
χ372-22-222-2-22-2002-22-1112-2-2-100-1i3−i3i3−i311-12-2-112-22-2000000i3i3−i3−i300i3−i3i3−i3-11000000000-11-11000000i3−i30000
χ382-22-222-2-22-2002-22-1112-2-2-100-1i3−i3i3−i311-12-2-11-22-22000000−i3−i3i3i300i3−i3i3−i3-110000000001-11-1000000−i3i30000
χ392-22-22-22-22-200-2222-2-22-2-220020000-2-22-22-222-2-220000000000000000-220000000002-2-22000000000000
χ402-22-22-22-22-200-2222-2-22-2-220020000-2-22-22-22-222-20000000000000000-22000000000-222-2000000000000
χ412-22-22-22-22-200-222-1112-2-2-100-1−i3i3i3−i311-1-221-12-2-22000000−i3−i3i3i300−i3i3i3−i31-1000000000-111-1000000i3−i30000
χ422-22-22-22-22-200-222-1112-2-2-100-1−i3i3i3−i311-1-221-1-222-2000000i3i3−i3−i300−i3i3i3−i31-10000000001-1-11000000−i3i30000
χ432-22-22-22-22-200-222-1112-2-2-100-1i3−i3−i3i311-1-221-12-2-22000000i3i3−i3−i300i3−i3−i3i31-1000000000-111-1000000−i3i30000
χ442-22-22-22-22-200-222-1112-2-2-100-1i3−i3−i3i311-1-221-1-222-2000000−i3−i3i3i300i3−i3−i3i31-10000000001-1-11000000i3−i30000
χ452-2-22200-2-220000222-2-22-2-200200002-2-2000000002-22-22-22-22-20000000000000002-20000002-200000000
χ462-2-22200-2-220000222-2-22-2-200200002-2-2000000002-2-22-222-22-2000000000000000-22000000-2200000000
χ472-2-22200-2-220000222-2-22-2-200200002-2-200000000-222-2-22-22-220000000000000002-2000000-2200000000
χ482-2-22200-2-220000222-2-22-2-200200002-2-200000000-22-222-2-22-22000000000000000-220000002-200000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-412222111-2-2-2-20000000000000022-1-1-1-1110000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-222111222200000000000000-2211-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-44122-2-21112222000000000000002-2-1-111-1-10000000000000000000000000
χ5344-4-44004-4-4000044-44-4-44-40040000-44-4000000000000000000000000000000000000000000000000000
χ5444-4-44004-4-400004-22-2-4-44200-200002-2200000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ5544-4-44004-4-400004-22-2-4-44200-200002-22000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ5644-4-44004-4-40000-24-4422-2-400-200002-220000000000000000000000000000000000000000000−2i32i3000000
χ5744-4-44004-4-40000-24-4422-2-400-200002-2200000000000000000000000000000000000000000002i3−2i3000000
χ584-44-444-4-44-4004-4-24-4-4-222400-2000022-2-224-400000000000000000000-220000000000000000000000000
χ594-44-444-4-44-4004-4-2-222-222-2001−2i32i3−2i32i3-1-11-22-220000000000000000i3−i3i3−i31-10000000000000000000000000
χ604-44-444-4-44-4004-4-2-222-222-20012i3−2i32i3−2i3-1-11-22-220000000000000000−i3i3−i3i31-10000000000000000000000000
χ614-44-44-44-44-400-44-24-4-4-222400-2000022-22-2-44000000000000000000002-20000000000000000000000000
χ624-44-44-44-44-400-44-2-222-222-2001−2i32i32i3−2i3-1-112-22-20000000000000000i3−i3−i3i3-110000000000000000000000000
χ634-44-44-44-44-400-44-2-222-222-20012i3−2i3−2i32i3-1-112-22-20000000000000000−i3i3i3−i3-110000000000000000000000000
χ644-4-44400-4-4400004-2-22-44-4200-20000-222000000004-40000-22-22000000000000000000000000000000000
χ654-4-44400-4-4400004-2-22-44-4200-20000-22200000000-4400002-22-2000000000000000000000000000000000
χ664-4-44400-4-440000-244-42-22-400-20000-2220000000000004-4000000000000000000000000000-2200000000
χ674-4-44400-4-440000-244-42-22-400-20000-222000000000000-440000000000000000000000000002-200000000
χ686666-366-3-3-366-3-300000000-3-300000000000000000022000000000000000000222-1-10000-1-100000000-1-1
χ696666-366-3-3-366-3-300000000-3-3000000000000000000-2-2000000000000000000-2-2-2110000110000000011
χ706666-366-3-3-3-6-6-3-30000000033000000000000000000220000000000000000002-2-2-1-10000-1-10000000011
χ716666-366-3-3-3-6-6-3-30000000033000000000000000000-2-2000000000000000000-2221100001100000000-1-1
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000022000000000000000000-22-2-1-100001100000000-11
χ736666-3-6-6-3-3-36-63300000000-33000000000000000000-2-20000000000000000002-22110000-1-1000000001-1
χ746666-3-6-6-3-3-3-6633000000003-300000000000000000022000000000000000000-2-22-1-1000011000000001-1
χ756666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-200000000000000000022-2110000-1-100000000-11
χ7688-8-88008-8-80000-4-44-444-440020000-22-2000000000000000000000000000000000000000000000000000
χ778-8-88800-8-880000-4-4-444-44400200002-2-2000000000000000000000000000000000000000000000000000
χ781212-12-12-600-666000000000000000000000000000000000000000000000000000000000000023−230000000000
χ791212-12-12-600-6660000000000000000000000000000000000000000000000000000000000000−23230000000000
χ8012-1212-12-612-126-6600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6-12126-66006-6000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-6000000000000000000000000000000004-4000000000000000000000-220000000000000000
χ8312-12-1212-60066-600000000000000000000000000000000-440000000000000000000002-20000000000000000

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