Finite Group Databasebeta

← Group #13140188

Character table — Group #13140188

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order12223446662466121212123366666612121212366666666666121212121212121212121212121288882424242424242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ51111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111
χ61111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ71111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1111-1-111-1-1
χ81111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-111-1-1-111-1-111
χ92222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000002020000-1-1-1-1
χ102222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000000-20-200001111
χ11222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222222222-2-2-2-222-2-22-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-11111000000000000020-2000011-1-1
χ142222222222-2-2-2-222-2-22-122-12-1-12222-1-2-211-1-11111-1-2-2-1-111-1-1-1-111110000000000000-2020000-1-111
χ152222222222-2-2-2-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-1111122-2-2-1-1-1-11111000000000000
χ162222222222-2-2-2-222-2-2-12-1-12-122-1-1-1-1-111-2-2-1-11111-11122-2-2-1-1-1-11111-2-2221111-1-1-1-1000000000000
χ1722222-2-22222-222-2-2-2-222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222-2-22222-222-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000−i3i3−i3i3
χ1922222-2-22222-222-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000i3−i3i3−i3
χ2022222-2-22222-222-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-211111111000033−3−333−3−3000000000000
χ2122222-2-22222-222-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-2111111110000−3−333−3−333000000000000
χ2222222-2-2222-22-2-2-2-22222222222-2-2-2-22-2-2-2-222-2-2-2-2222-2-222-2-2-2-22222000000000000000000000000
χ2322222-2-2222-22-2-2-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000−i3i3i3−i3
χ2422222-2-2222-22-2-2-2-2222-122-12-1-1-2-2-2-2-1-2-211-1-11111-12211-1-11111-1-1-1-100000000000000000000i3−i3−i3i3
χ2522222-2-2222-22-2-2-2-222-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-1000033−3−3−3−333000000000000
χ2622222-2-2222-22-2-2-2-222-12-1-12-1221111-111-2-2-1-11111-1-1-1-2-2221111-1-1-1-10000−3−33333−3−3000000000000
χ272-22-222-2-22-200002-20022-2-2-22-2222-2-220000-2-200002002-20022-2-20000002i−2i00002i−2i2i−2i000000000000
χ282-22-222-2-22-200002-20022-2-2-22-2222-2-220000-2-200002002-20022-2-2000000−2i2i0000−2i2i−2i2i000000000000
χ292-22-222-2-22-200002-200-1211-2-1-22-1-111-1−i3i30011−i3−i3i3i3-1−i3i32-200-1-111−i3−i3i3i3002i−2i3−33−3−ii−ii000000000000
χ302-22-222-2-22-200002-200-1211-2-1-22-1-111-1−i3i30011−i3−i3i3i3-1−i3i32-200-1-111−i3−i3i3i300−2i2i−33−33i−ii−i000000000000
χ312-22-222-2-22-200002-200-1211-2-1-22-1-111-1i3−i30011i3i3−i3−i3-1i3−i32-200-1-111i3i3−i3−i3002i−2i−33−33−ii−ii000000000000
χ322-22-222-2-22-200002-200-1211-2-1-22-1-111-1i3−i30011i3i3−i3−i3-1i3−i32-200-1-111i3i3−i3−i300−2i2i3−33−3i−ii−i000000000000
χ332-22-22-22-22-20000-220022-2-2-22-22-2-22220000-2-20000200-2200-2-22200002-2002-2-220000000000000000
χ342-22-22-22-22-20000-220022-2-2-22-22-2-22220000-2-20000200-2200-2-2220000-2200-222-20000000000000000
χ352-22-22-22-22-20000-2200-1211-2-1-2211-1-1-1−i3i30011−i3−i3i3i3-1i3−i3-220011-1-1i3i3−i3−i32-200-111-1−i3i3i3−i3000000000000
χ362-22-22-22-22-20000-2200-1211-2-1-2211-1-1-1−i3i30011−i3−i3i3i3-1i3−i3-220011-1-1i3i3−i3−i3-22001-1-11i3−i3−i3i3000000000000
χ372-22-22-22-22-20000-2200-1211-2-1-2211-1-1-1i3−i30011i3i3−i3−i3-1−i3i3-220011-1-1−i3−i3i3i32-200-111-1i3−i3−i3i3000000000000
χ382-22-22-22-22-20000-2200-1211-2-1-2211-1-1-1i3−i30011i3i3−i3−i3-1−i3i3-220011-1-1−i3−i3i3i3-22001-1-11−i3i3i3−i3000000000000
χ39444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000
χ404444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000
χ4144444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000
χ4244444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000
χ4344-4-44004-4-400000000444-44-4-4-40000400004-40000-400000000000000000000000000000000000000
χ4444-4-44004-4-4000000004-24-4-2-4220000-200−2i32i3-22−2i32i3−2i32i3200000000000000000000000000000000000000
χ4544-4-44004-4-4000000004-24-4-2-4220000-2002i3−2i3-222i3−2i32i3−2i3200000000000000000000000000000000000000
χ4644-4-44004-4-400000000-24-2242-4-423−2323−23-20000-220000200000023−2323−230000000000000000000000000000
χ4744-4-44004-4-400000000-24-2242-4-4−2323−2323-20000-2200002000000−2323−23230000000000000000000000000000
χ4844-4-44004-4-400000000-2-2-22-222223−2323−23100−2i32i31-1i3−i3i3−i3-1000000−33−333i−3i3i−3i000000000000000000000000
χ4944-4-44004-4-400000000-2-2-22-222223−2323−231002i3−2i31-1−i3i3−i3i3-1000000−33−33−3i3i−3i3i000000000000000000000000
χ5044-4-44004-4-400000000-2-2-22-2222−2323−2323100−2i32i31-1i3−i3i3−i3-10000003−33−3−3i3i−3i3i000000000000000000000000
χ5144-4-44004-4-400000000-2-2-22-2222−2323−23231002i3−2i31-1−i3i3−i3i3-10000003−33−33i−3i3i−3i000000000000000000000000
χ524-44-444-4-44-400004-4004-2-4-4242-244-4-4-20000220000-200-2200-2-2220000000000000000000000000000
χ534-44-444-4-44-400004-400-2-2222-22-2-2-2221−2i32i300-1-1i3i3−i3−i31−2i32i3-220011-1-1i3i3−i3−i3000000000000000000000000
χ544-44-444-4-44-400004-400-2-2222-22-2-2-22212i3−2i300-1-1−i3−i3i3i312i3−2i3-220011-1-1−i3−i3i3i3000000000000000000000000
χ554-44-44-44-44-40000-44004-2-4-4242-2-4-444-20000220000-2002-20022-2-20000000000000000000000000000
χ564-44-44-44-44-40000-4400-2-2222-22-222-2-21−2i32i300-1-1i3i3−i3−i312i3−2i32-200-1-111−i3−i3i3i3000000000000000000000000
χ574-44-44-44-44-40000-4400-2-2222-22-222-2-212i3−2i300-1-1−i3−i3i3i31−2i32i32-200-1-111i3i3−i3−i3000000000000000000000000
χ584-4-44400-4-440000000044-44-4-44-4000040000-440000-400000000000000000000000000000000000000
χ594-4-44400-4-44000000004-2-442-4-220000-200002-200002000023−23000023−23−2323000000000000000000000000
χ604-4-44400-4-44000000004-2-442-4-220000-200002-2000020000−23230000−232323−23000000000000000000000000
χ614-4-44400-4-4400000000-242-2-424-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000
χ624-4-44400-4-4400000000-242-2-424-4−232323−23-200002-200002000000−232323−230000000000000000000000000000
χ634-4-44400-4-4400000000-2-22-222-2223−23−232310000-113-3-33-1000023−23−333−3−333−3000000000000000000000000
χ644-4-44400-4-4400000000-2-22-222-2223−23−232310000-11-333-3-10000−2323−333−33−3−33000000000000000000000000
χ654-4-44400-4-4400000000-2-22-222-22−232323−2310000-113-3-33-10000−23233−3−333−3−33000000000000000000000000
χ664-4-44400-4-4400000000-2-22-222-22−232323−2310000-11-333-3-1000023−233−3−33−333−3000000000000000000000000
χ676666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000000000002020-1-1-1-10000
χ686666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000000000-20-2011110000
χ696666-366-3-3-3-6-633-3-3330000000000000000000000000000000000000000000000000020-20-1-1110000
χ706666-366-3-3-3-6-633-3-33300000000000000000000000000000000000000000000000000-202011-1-10000
χ716666-3-6-6-3-3-36-6-3-33333000000000000000000000000000000000000000000000000000000−i3i3−i3i30000
χ726666-3-6-6-3-3-36-6-3-33333000000000000000000000000000000000000000000000000000000i3−i3i3−i30000
χ736666-3-6-6-3-3-3-663333-3-3000000000000000000000000000000000000000000000000000000−i3i3i3−i30000
χ746666-3-6-6-3-3-3-663333-3-3000000000000000000000000000000000000000000000000000000i3−i3−i3i30000
χ751212-12-12-600-66600000063−6300000000000000000000000000000000000000000000000000000000000000
χ761212-12-12-600-666000000−636300000000000000000000000000000000000000000000000000000000000000
χ7712-1212-12-612-126-660000-660000000000000000000000000000000000000000000000000000000000000000
χ7812-1212-12-6-12126-6600006-60000000000000000000000000000000000000000000000000000000000000000
χ7912-12-1212-60066-600−6i36i3000000000000000000000000000000000000000000000000000000000000000000
χ8012-12-1212-60066-6006i3−6i3000000000000000000000000000000000000000000000000000000000000000000

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