Finite Group Databasebeta

← Group #13150609

Character table — Group #13150609

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666246612121212336666661212121236666666666612121212121212121212121212124444444444444412121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ61111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1
χ71111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ81111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111
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
χ1011111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11-11-1111-1-111-1-1-11-11-11-11
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-11-1-111-1-1111-11-1-11-11
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-111-1-1-111-1-111-11-111-11-1
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-1111111-1-1-111-1-11-111-111-1-1-1-1111-1-11-111-1
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-1111111-1-1-11-111-11-1-1111-1-1-1-111-111-11-1-11
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-1111-11-11-1-11-11-1-11111-1-11-1-111-1-11
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-1111-1-11-111-11-1-1-11111-1-1-111-1-111-1
χ172222222222222222222-12-12-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-100000000
χ182222222222222222222-12-12-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111111100000000
χ19222222222222222222-12-12-122-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000220022000000000000-1-1-1-1
χ20222222222222222222-12-12-122-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-200-2-20000000000001111
χ212222222222-2-2-2-222-2-22-12-12-1-12-1-1-1-1-1-2-211-1-11111-11122-2-2-1-1-1-111112222-2-200000000-1-1-1-1111100000000
χ222222222222-2-2-2-222-2-22-12-12-1-12-1-1-1-1-1-2-211-1-11111-11122-2-2-1-1-1-11111-2-2-2-222000000001111-1-1-1-100000000
χ232222222222-2-2-2-222-2-2-12-12-122-12222-111-2-2-1-11111-1-2-2-1-111-1-1-1-11111000000002200-2-2000000000000-1-111
χ242222222222-2-2-2-222-2-2-12-12-122-12222-111-2-2-1-11111-1-2-2-1-111-1-1-1-1111100000000-2-2002200000000000011-1-1
χ2522222-2-22222-222-2-2-2-22-12-12-1-121111-122-1-1-1-1-1-1-1-1-111-2-2-2-21111111122-2-22-200000000-1-111-1-11100000000
χ2622222-2-22222-222-2-2-2-22-12-12-1-121111-122-1-1-1-1-1-1-1-1-111-2-2-2-211111111-2-222-220000000011-1-111-1-100000000
χ2722222-2-22222-222-2-2-2-2-12-12-122-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-2111111111111000000002-2002-2000000000000-11-11
χ2822222-2-22222-222-2-2-2-2-12-12-122-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-211111111111100000000-2200-220000000000001-11-1
χ2922222-2-2222-22-2-2-2-2222-12-12-1-121111-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-122-2-2-2200000000-1-11111-1-100000000
χ3022222-2-2222-22-2-2-2-2222-12-12-1-121111-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-1-2-2222-20000000011-1-1-1-11100000000
χ3122222-2-2222-22-2-2-2-222-12-12-122-1-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-1000000002-200-22000000000000-111-1
χ3222222-2-2222-22-2-2-2-222-12-12-122-1-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-100000000-22002-20000000000001-1-11
χ332-2-2222-2-2-2200002-20022-22-2-2-2222-2-220000-2-200002002-20022-2-200002i−2i2i−2i00000000002i−2i2i−2i000000000000
χ342-2-2222-2-2-2200002-20022-22-2-2-2222-2-220000-2-200002002-20022-2-20000−2i2i−2i2i0000000000−2i2i−2i2i000000000000
χ352-2-2222-2-2-2200002-2002-1-2-1-2112-1-111-100−i3i311−i3−i3i3i3-1−i3i32-200-1-111−i3−i3i3i32i−2i2i−2i0000000000−ii−ii3−33−300000000
χ362-2-2222-2-2-2200002-2002-1-2-1-2112-1-111-100−i3i311−i3−i3i3i3-1−i3i32-200-1-111−i3−i3i3i3−2i2i−2i2i0000000000i−ii−i−33−3300000000
χ372-2-2222-2-2-2200002-2002-1-2-1-2112-1-111-100i3−i311i3i3−i3−i3-1i3−i32-200-1-111i3i3−i3−i32i−2i2i−2i0000000000−ii−ii−33−3300000000
χ382-2-2222-2-2-2200002-2002-1-2-1-2112-1-111-100i3−i311i3i3−i3−i3-1i3−i32-200-1-111i3i3−i3−i3−2i2i−2i2i0000000000i−ii−i3−33−300000000
χ392-2-222-22-2-220000-220022-22-2-2-22-2-22220000-2-20000200-2200-2-22200002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ402-2-222-22-2-220000-220022-22-2-2-22-2-22220000-2-20000200-2200-2-2220000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ412-2-222-22-2-220000-22002-1-2-1-211211-1-1-100−i3i311−i3−i3i3i3-1i3−i3-220011-1-1i3i3−i3−i32i−2i−2i2i0000000000−iii−i3−3−3300000000
χ422-2-222-22-2-220000-22002-1-2-1-211211-1-1-100−i3i311−i3−i3i3i3-1i3−i3-220011-1-1i3i3−i3−i3−2i2i2i−2i0000000000i−i−ii−333−300000000
χ432-2-222-22-2-220000-22002-1-2-1-211211-1-1-100i3−i311i3i3−i3−i3-1−i3i3-220011-1-1−i3−i3i3i32i−2i−2i2i0000000000−iii−i−333−300000000
χ442-2-222-22-2-220000-22002-1-2-1-211211-1-1-100i3−i311i3i3−i3−i3-1−i3i3-220011-1-1−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
χ464444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000
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
χ4844444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4944-4-44004-4-40000000044-4-444-4-40000400004-40000-400000000000000000000000000000000000000000000
χ5044-4-44004-4-4000000004-2-424-22-423−2323−23-20000-220000200000023−2323−230000000000000000000000000000000000
χ5144-4-44004-4-4000000004-2-424-22-4−2323−2323-20000-2200002000000−2323−23230000000000000000000000000000000000
χ5244-4-44004-4-400000000-242-4-24-420000-20000-2200002000023−23000023−2323−23000000000000000000000000000000
χ5344-4-44004-4-400000000-242-4-24-420000-20000-22000020000−23230000−2323−2323000000000000000000000000000000
χ5444-4-44004-4-400000000-2-222-2-22223−2323−23100001-13-33-3-1000023−23−33−33−33−33000000000000000000000000000000
χ5544-4-44004-4-400000000-2-222-2-22223−2323−23100001-1-33-33-10000−2323−33−333−33−3000000000000000000000000000000
χ5644-4-44004-4-400000000-2-222-2-222−2323−2323100001-13-33-3-10000−23233−33−33−33−3000000000000000000000000000000
χ5744-4-44004-4-400000000-2-222-2-222−2323−2323100001-1-33-33-1000023−233−33−3−33−33000000000000000000000000000000
χ584-44-4400-44-400000000444-4-4-44-4000040000-440000-400000000000000000000000000000000000000000000
χ594-44-4400-44-4000000004-242-42-2-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ604-44-4400-44-4000000004-242-42-2-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ614-44-4400-44-400000000-24-2-42-4420000-2−2i32i3002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000
χ624-44-4400-44-400000000-24-2-42-4420000-22i3−2i3002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000
χ634-44-4400-44-400000000-2-2-2222-2223−23−23231−2i32i300-11i3−i3−i3i3-1000000−333−33i−3i−3i3i000000000000000000000000000000
χ644-44-4400-44-400000000-2-2-2222-2223−23−232312i3−2i300-11−i3i3i3−i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000
χ654-44-4400-44-400000000-2-2-2222-22−232323−231−2i32i300-11i3−i3−i3i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000
χ664-44-4400-44-400000000-2-2-2222-22−232323−2312i3−2i300-11−i3i3i3−i3-10000003−3−333i−3i−3i3i000000000000000000000000000000
χ674-4-4444-4-4-4400004-400-24242-4-4-244-4-4-20000220000-200-2200-2-2220000000000000000000000000000000000
χ684-4-4444-4-4-4400004-400-2-22-2222-2-2-222100−2i32i3-1-1i3i3−i3−i31−2i32i3-220011-1-1i3i3−i3−i3000000000000000000000000000000
χ694-4-4444-4-4-4400004-400-2-22-2222-2-2-2221002i3−2i3-1-1−i3−i3i3i312i3−2i3-220011-1-1−i3−i3i3i3000000000000000000000000000000
χ704-4-444-44-4-440000-4400-24242-4-4-2-4-444-20000220000-2002-20022-2-20000000000000000000000000000000000
χ714-4-444-44-4-440000-4400-2-22-2222-222-2-2100−2i32i3-1-1i3i3−i3−i312i3−2i32-200-1-111−i3−i3i3i3000000000000000000000000000000
χ724-4-444-44-4-440000-4400-2-22-2222-222-2-21002i3−2i3-1-1−i3−i3i3i31−2i32i32-200-1-111i3i3−i3−i3000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000002200220000000000-1-1-1-10000
χ746666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000-2-200-2-2000000000011110000
χ756666-366-3-3-3-6-633-3-333000000000000000000000000000000000000000000002200-2-20000000000-1-1110000
χ766666-366-3-3-3-6-633-3-33300000000000000000000000000000000000000000000-2-20022000000000011-1-10000
χ776666-3-6-6-3-3-36-6-3-33333000000000000000000000000000000000000000000002-2002-20000000000-11-110000
χ786666-3-6-6-3-3-36-6-3-3333300000000000000000000000000000000000000000000-2200-2200000000001-11-10000
χ796666-3-6-6-3-3-3-663333-3-3000000000000000000000000000000000000000000002-200-220000000000-111-10000
χ806666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000000-22002-200000000001-1-110000
χ811212-12-12-600-66600−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-600-666006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6006-6600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-6006-66000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-612-1266-60000-660000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-6-121266-600006-60000000000000000000000000000000000000000000000000000000000000000000000

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