Finite Group Databasebeta

← Group #13150863

Character table — Group #13150863

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order122234466624661212121233666666121212123666666666661212121212121212121212121212444422224444441212121212121212666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111
χ61111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1
χ71111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ81111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111
χ911111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-11-11-111-1-111-1-11-11-11-11-1
χ1011111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-111-1-11-1111-1-111-1-1-11-11-11-11
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-111-1-11-1-111-1-1111-1-111-1-11
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-111-1-1-111-1-111-111-1-111-1
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-11-1-11-11-111-111-1-1-1-1111-1-11-111-1
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-111-1-111-1-1111-1-1-1-111-111-11-1-11
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1111-11-11-1-11-11-1-11111-1-11-11-1-11-11
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-11-111-11-11-1-1-11111-1-1-11-111-11-1
χ172222222222222222222-1-12-122-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000220000220000000000-1-100-1-1
χ182222222222222222222-1-12-122-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000-2-20000-2-20000000000110011
χ19222222222222222222-122-12-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220000220000-1-1-1-1-1-1-1-100000000
χ20222222222222222222-122-12-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-200001111111100000000
χ212222222222-2-2-2-222-2-22-1-12-122-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000220000-2-20000000000-1-10011
χ222222222222-2-2-2-222-2-22-1-12-122-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-11111000000-2-200002200000000001100-1-1
χ232222222222-2-2-2-222-2-2-122-12-1-12-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-1111122220000-2-20000-1-1-1-1111100000000
χ242222222222-2-2-2-222-2-2-122-12-1-12-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-11111-2-2-2-200002200001111-1-1-1-100000000
χ2522222-2-22222-222-2-2-2-22-1-12-122-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-211111111110000002-200002-20000000000-1100-11
χ2622222-2-22222-222-2-2-2-22-1-12-122-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-21111111111000000-220000-2200000000001-1001-1
χ2722222-2-22222-222-2-2-2-2-122-12-1-121111-1-1-122-1-1-1-1-1-1-1-2-211-2-21111111122-2-200002-20000-1-111-1-11100000000
χ2822222-2-22222-222-2-2-2-2-122-12-1-121111-1-1-122-1-1-1-1-1-1-1-2-211-2-211111111-2-2220000-22000011-1-111-1-100000000
χ2922222-2-2222-22-2-2-2-2222-1-12-122-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-10000002-20000-220000000000-11001-1
χ3022222-2-2222-22-2-2-2-2222-1-12-122-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-1000000-2200002-200000000001-100-11
χ3122222-2-2222-22-2-2-2-222-122-12-1-121111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-122-2-20000-220000-1-11111-1-100000000
χ3222222-2-2222-22-2-2-2-222-122-12-1-121111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-1-2-22200002-2000011-1-1-1-11100000000
χ3322-2-222-2-22-200002-20022-222-2-2-222-2-220000-2-2000022-2000022-2-200002i−2i2i−2i00000000002i−2i2i−2i000000000000
χ3422-2-222-2-22-200002-20022-222-2-2-222-2-220000-2-2000022-2000022-2-20000−2i2i−2i2i0000000000−2i2i−2i2i000000000000
χ3522-2-222-2-22-200002-200-12-2-1211-2-1-111-1−i3i30011−i3−i3i3i3-12-2−i3i300-1-111−i3−i3i3i32i−2i2i−2i0000000000−ii−ii3−33−300000000
χ3622-2-222-2-22-200002-200-12-2-1211-2-1-111-1−i3i30011−i3−i3i3i3-12-2−i3i300-1-111−i3−i3i3i3−2i2i−2i2i0000000000i−ii−i−33−3300000000
χ3722-2-222-2-22-200002-200-12-2-1211-2-1-111-1i3−i30011i3i3−i3−i3-12-2i3−i300-1-111i3i3−i3−i32i−2i2i−2i0000000000−ii−ii−33−3300000000
χ3822-2-222-2-22-200002-200-12-2-1211-2-1-111-1i3−i30011i3i3−i3−i3-12-2i3−i300-1-111i3i3−i3−i3−2i2i−2i2i0000000000i−ii−i3−33−300000000
χ3922-2-22-22-22-20000-220022-222-2-2-2-2-22220000-2-200002-220000-2-22200002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ4022-2-22-22-22-20000-220022-222-2-2-2-2-22220000-2-200002-220000-2-2220000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ4122-2-22-22-22-20000-2200-12-2-1211-211-1-1-1−i3i30011−i3−i3i3i3-1-22i3−i30011-1-1i3i3−i3−i32i−2i−2i2i0000000000−iii−i3−3−3300000000
χ4222-2-22-22-22-20000-2200-12-2-1211-211-1-1-1−i3i30011−i3−i3i3i3-1-22i3−i30011-1-1i3i3−i3−i3−2i2i2i−2i0000000000i−i−ii−333−300000000
χ4322-2-22-22-22-20000-2200-12-2-1211-211-1-1-1i3−i30011i3i3−i3−i3-1-22−i3i30011-1-1−i3−i3i3i32i−2i−2i2i0000000000−iii−i−333−300000000
χ4422-2-22-22-22-20000-2200-12-2-1211-211-1-1-1i3−i30011i3i3−i3−i3-1-22−i3i30011-1-1−i3−i3i3i3−2i2i2i−2i0000000000i−i−ii3−3−3300000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ464444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000
χ4744444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4844444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ4944-4-444-4-44-400004-4004-224-2-4-4244-4-4-20000220000-2-220000-2-2220000000000000000000000000000000000
χ5044-4-444-4-44-400004-400-2-22-2-2222-2-2221−2i32i300-1-1i3i3−i3−i31-22−2i32i30011-1-1i3i3−i3−i3000000000000000000000000000000
χ5144-4-444-4-44-400004-400-2-22-2-2222-2-22212i3−2i300-1-1−i3−i3i3i31-222i3−2i30011-1-1−i3−i3i3i3000000000000000000000000000000
χ5244-4-44-44-44-40000-44004-224-2-4-42-4-444-20000220000-22-2000022-2-20000000000000000000000000000000000
χ5344-4-44-44-44-40000-4400-2-22-2-222222-2-21−2i32i300-1-1i3i3−i3−i312-22i3−2i300-1-111−i3−i3i3i3000000000000000000000000000000
χ5444-4-44-44-44-40000-4400-2-22-2-222222-2-212i3−2i300-1-1−i3−i3i3i312-2−2i32i300-1-111i3i3−i3−i3000000000000000000000000000000
χ554-44-44004-4-40000000044-4-4-44-440000400004-40000-400000000000000000000000000000000000000000000
χ564-44-44004-4-4000000004-22-424-4-20000-200−2i32i3-22−2i32i3−2i32i3200000000000000000000000000000000000000000000
χ574-44-44004-4-4000000004-22-424-4-20000-2002i3−2i3-222i3−2i32i3−2i3200000000000000000000000000000000000000000000
χ584-44-44004-4-400000000-24-42-4-22423−2323−23-20000-220000200000023−2323−230000000000000000000000000000000000
χ594-44-44004-4-400000000-24-42-4-224−2323−2323-20000-2200002000000−2323−23230000000000000000000000000000000000
χ604-44-44004-4-400000000-2-2222-22-223−2323−23100−2i32i31-1i3−i3i3−i3-1000000−33−333i−3i3i−3i000000000000000000000000000000
χ614-44-44004-4-400000000-2-2222-22-223−2323−231002i3−2i31-1−i3i3−i3i3-1000000−33−33−3i3i−3i3i000000000000000000000000000000
χ624-44-44004-4-400000000-2-2222-22-2−2323−2323100−2i32i31-1i3−i3i3−i3-10000003−33−3−3i3i−3i3i000000000000000000000000000000
χ634-44-44004-4-400000000-2-2222-22-2−2323−23231002i3−2i31-1−i3i3−i3i3-10000003−33−33i−3i3i−3i000000000000000000000000000000
χ644-4-44400-4-4400000000444-4-4-44-4000040000-440000-400000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-2-42-4420000-200002-200002000023−23000023−23−2323000000000000000000000000000000
χ664-4-44400-4-44000000004-2-2-42-4420000-200002-2000020000−23230000−232323−23000000000000000000000000000000
χ674-4-44400-4-4400000000-2442-42-2-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ684-4-44400-4-4400000000-2442-42-2-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ694-4-44400-4-4400000000-2-2-2222-2223−23−232310000-113-3-33-1000023−23−333−3−333−3000000000000000000000000000000
χ704-4-44400-4-4400000000-2-2-2222-2223−23−232310000-11-333-3-10000−2323−333−33−3−33000000000000000000000000000000
χ714-4-44400-4-4400000000-2-2-2222-22−232323−2310000-113-3-33-10000−23233−3−333−3−33000000000000000000000000000000
χ724-4-44400-4-4400000000-2-2-2222-22−232323−2310000-11-333-3-1000023−233−3−33−333−3000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000220000220000000000-1-100-1-100
χ746666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000-2-20000-2-2000000000011001100
χ756666-366-3-3-3-6-633-3-333000000000000000000000000000000000000000000220000-2-20000000000-1-1001100
χ766666-366-3-3-3-6-633-3-333000000000000000000000000000000000000000000-2-200002200000000001100-1-100
χ776666-3-6-6-3-3-36-6-3-333330000000000000000000000000000000000000000002-200002-20000000000-1100-1100
χ786666-3-6-6-3-3-36-6-3-33333000000000000000000000000000000000000000000-220000-2200000000001-1001-100
χ796666-3-6-6-3-3-3-663333-3-30000000000000000000000000000000000000000002-20000-220000000000-11001-100
χ806666-3-6-6-3-3-3-663333-3-3000000000000000000000000000000000000000000-2200002-200000000001-100-1100
χ811212-12-12-612-126-660000-660000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-12126-6600006-60000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-66600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-600-666000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-600−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-6006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000

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