Finite Group Databasebeta

← Group #13150835

Character table — Group #13150835

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666246612121212336666661212121236666666666612121212121212121212121212122244222444444466661212121266121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-111-1-111-1-1-1-111
χ61111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-111-1-111-1-1-1-11111-1-1
χ71111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-111-1-1
χ81111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1111-1-111-1-111-1-111-1-111
χ911111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-111-111-1-1-1-1111-11-11-11-1
χ1011111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1111-1-1-1-111-11-11-11-11
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-1-11-1-11111-1-11-11-1-11-11
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-111-1-11-1-1-11111-1-1-11-111-11-1
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-111-1-11-11-11-11111-1-1-1-11-1-11-111-1
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-11-111-11-1-1-111111-1-1-1-1-111-11-1-11
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-11-1-111-11-11-1-1-1-111111-1-111-1-11
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-1-111-1-1111-1-1-1-1-11111-111-1-111-1
χ172222222222222222222-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122222000000200-1-1-1-1-1-1-1-100000000
χ182222222222222222222-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2000000-2001111111100000000
χ19222222222222222222-12-122-1-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000022022000000000000-1-1-1-1
χ20222222222222222222-12-122-1-122222-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000-2-20-2-20000000000001111
χ212222222222-2-2-2-222-2-22-12-1-122-1-1-1-1-1-1-2-211-1-11111-122-2-211-1-1-1-111112222-2000000-200-1-111-1-11100000000
χ222222222222-2-2-2-222-2-22-12-1-122-1-1-1-1-1-1-2-211-1-11111-122-2-211-1-1-1-11111-2-2-2-2200000020011-1-111-1-100000000
χ232222222222-2-2-2-222-2-2-12-122-1-122222-111-2-2-1-11111-1-1-111-2-2-1-1-1-11111000000000220-2-2000000000000-1-111
χ242222222222-2-2-2-222-2-2-12-122-1-122222-111-2-2-1-11111-1-1-111-2-2-1-1-1-11111000000000-2-202200000000000011-1-1
χ2522222-2-22222-222-2-2-2-22-12-1-122-11111-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111122-2-2-2000000200-1-11111-1-100000000
χ2622222-2-22222-222-2-2-2-22-12-1-122-11111-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111-2-2222000000-20011-1-1-1-11100000000
χ2722222-2-22222-222-2-2-2-2-12-122-1-12-2-2-2-2-1-1-122-1-1-1-1-1-1-11111-2-2111111110000000002-202-2000000000000-11-11
χ2822222-2-22222-222-2-2-2-2-12-122-1-12-2-2-2-2-1-1-122-1-1-1-1-1-1-11111-2-211111111000000000-220-220000000000001-11-1
χ2922222-2-2222-22-2-2-2-2222-12-1-122-11111-1-2-211-1-11111-1-2-222-1-11111-1-1-1-122-2-22000000-200-1-1-1-1111100000000
χ3022222-2-2222-22-2-2-2-2222-12-1-122-11111-1-2-211-1-11111-1-2-222-1-11111-1-1-1-1-2-222-20000002001111-1-1-1-100000000
χ3122222-2-2222-22-2-2-2-222-12-122-1-12-2-2-2-2-111-2-2-1-11111-111-1-1221111-1-1-1-10000000002-20-22000000000000-111-1
χ3222222-2-2222-22-2-2-2-222-12-122-1-12-2-2-2-2-111-2-2-1-11111-111-1-1221111-1-1-1-1000000000-2202-20000000000001-1-11
χ332-2-2222-2-22-200002-20022-2-2-2-22222-2-220000-2-2000022-2000022-2-200002-22-200000000002-2002-20000000000
χ342-2-2222-2-22-200002-20022-2-2-2-22222-2-220000-2-2000022-2000022-2-20000-22-220000000000-2200-220000000000
χ352-2-2222-2-22-200002-2002-1-211-22-1-1-111-100−i3i311−i3−i3i3i3-12-200−i3i3-1-111−i3−i3i3i32-22-20000000000-11−i3i3-11−i3i300000000
χ362-2-2222-2-22-200002-2002-1-211-22-1-1-111-100−i3i311−i3−i3i3i3-12-200−i3i3-1-111−i3−i3i3i3-22-2200000000001-1i3−i31-1i3−i300000000
χ372-2-2222-2-22-200002-2002-1-211-22-1-1-111-100i3−i311i3i3−i3−i3-12-200i3−i3-1-111i3i3−i3−i32-22-20000000000-11i3−i3-11i3−i300000000
χ382-2-2222-2-22-200002-2002-1-211-22-1-1-111-100i3−i311i3i3−i3−i3-12-200i3−i3-1-111i3i3−i3−i3-22-2200000000001-1−i3i31-1−i3i300000000
χ392-2-222-22-22-20000-220022-2-2-2-222-2-22220000-2-200002-220000-2-22200002-2-2200000000002-200-220000000000
χ402-2-222-22-22-20000-220022-2-2-2-222-2-22220000-2-200002-220000-2-2220000-222-20000000000-22002-20000000000
χ412-2-222-22-22-20000-22002-1-211-22-111-1-1-100−i3i311−i3−i3i3i3-1-2200i3−i311-1-1i3i3−i3−i32-2-220000000000-11i3−i31-1−i3i300000000
χ422-2-222-22-22-20000-22002-1-211-22-111-1-1-100−i3i311−i3−i3i3i3-1-2200i3−i311-1-1i3i3−i3−i3-222-200000000001-1−i3i3-11i3−i300000000
χ432-2-222-22-22-20000-22002-1-211-22-111-1-1-100i3−i311i3i3−i3−i3-1-2200−i3i311-1-1−i3−i3i3i32-2-220000000000-11−i3i31-1i3−i300000000
χ442-2-222-22-22-20000-22002-1-211-22-111-1-1-100i3−i311i3i3−i3−i3-1-2200−i3i311-1-1−i3−i3i3i3-222-200000000001-1i3−i3-11−i3i300000000
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
χ4944-4-44004-4-4000000004444-4-4-4-40000400004-40000-400000000000000000000000000000000000000000000
χ5044-4-44004-4-4000000004-24-22-4-4223−2323−23-20000-220000200000023−2323−230000000000000000000000000000000000
χ5144-4-44004-4-4000000004-24-22-4-42−2323−2323-20000-2200002000000−2323−23230000000000000000000000000000000000
χ5244-4-44004-4-400000000-24-24-422-40000-2−2i32i300-22−2i32i3−2i32i3200000000000000000000000000000000000000000000
χ5344-4-44004-4-400000000-24-24-422-40000-22i3−2i300-222i3−2i32i3−2i3200000000000000000000000000000000000000000000
χ5444-4-44004-4-400000000-2-2-2-2222223−2323−231−2i32i3001-1i3−i3i3−i3-1000000−33−333i−3i3i−3i000000000000000000000000000000
χ5544-4-44004-4-400000000-2-2-2-2222223−2323−2312i3−2i3001-1−i3i3−i3i3-1000000−33−33−3i3i−3i3i000000000000000000000000000000
χ5644-4-44004-4-400000000-2-2-2-22222−2323−23231−2i32i3001-1i3−i3i3−i3-10000003−33−3−3i3i−3i3i000000000000000000000000000000
χ5744-4-44004-4-400000000-2-2-2-22222−2323−232312i3−2i3001-1−i3i3−i3i3-10000003−33−33i−3i3i−3i000000000000000000000000000000
χ584-44-4400-4-440000000044-4-444-4-4000040000-440000-400000000000000000000000000000000000000000000
χ594-44-4400-4-44000000004-2-42-24-4223−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000
χ604-44-4400-4-44000000004-2-42-24-42−232323−23-200002-200002000000−232323−230000000000000000000000000000000000
χ614-44-4400-4-4400000000-242-44-22-40000-200002-2000020023−2300000023−23−2323000000000000000000000000000000
χ624-44-4400-4-4400000000-242-44-22-40000-200002-20000200−2323000000−232323−23000000000000000000000000000000
χ634-44-4400-4-4400000000-2-222-2-22223−23−232310000-113-3-33-10023−2300−333−3−333−3000000000000000000000000000000
χ644-44-4400-4-4400000000-2-222-2-22223−23−232310000-11-333-3-100−232300−333−33−3−33000000000000000000000000000000
χ654-44-4400-4-4400000000-2-222-2-222−232323−2310000-113-3-33-100−2323003−3−333−3−33000000000000000000000000000000
χ664-44-4400-4-4400000000-2-222-2-222−232323−2310000-11-333-3-10023−23003−3−33−333−3000000000000000000000000000000
χ674-4-4444-4-44-400004-400-242-4-42-2444-4-4-20000220000-2-220000-2-2220000000000000000000000000000000000
χ684-4-4444-4-44-400004-400-2-22222-2-2-2-222100−2i32i3-1-1i3i3−i3−i31-2200−2i32i311-1-1i3i3−i3−i3000000000000000000000000000000
χ694-4-4444-4-44-400004-400-2-22222-2-2-2-2221002i3−2i3-1-1−i3−i3i3i31-22002i3−2i311-1-1−i3−i3i3i3000000000000000000000000000000
χ704-4-444-44-44-40000-4400-242-4-42-24-4-444-20000220000-22-2000022-2-20000000000000000000000000000000000
χ714-4-444-44-44-40000-4400-2-22222-2-222-2-2100−2i32i3-1-1i3i3−i3−i312-2002i3−2i3-1-111−i3−i3i3i3000000000000000000000000000000
χ724-4-444-44-44-40000-4400-2-22222-2-222-2-21002i3−2i3-1-1−i3−i3i3i312-200−2i32i3-1-111i3i3−i3−i3000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000022220000000000000-1-1-1-10000
χ746666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000-2-2-2-2000000000000011110000
χ756666-366-3-3-3-6-633-3-333000000000000000000000000000000000000000000022-2-20000000000000-1-1110000
χ766666-366-3-3-3-6-633-3-3330000000000000000000000000000000000000000000-2-222000000000000011-1-10000
χ776666-3-6-6-3-3-36-6-3-3333300000000000000000000000000000000000000000002-22-20000000000000-11-110000
χ786666-3-6-6-3-3-36-6-3-333330000000000000000000000000000000000000000000-22-2200000000000001-11-10000
χ796666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000002-2-220000000000000-111-10000
χ806666-3-6-6-3-3-3-663333-3-30000000000000000000000000000000000000000000-222-200000000000001-1-110000
χ811212-12-12-600-66600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-600-666000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-60066-600−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-60066-6006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-612-126-660000-660000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-6-12126-6600006-60000000000000000000000000000000000000000000000000000000000000000000000

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