Finite Group Databasebeta

← Group #13147800

Character table — Group #13147800

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666441212121212123366666612121212366612121212121212121212121212121212121212121212444424444444441212121212121212612121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1
χ51111111111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-11-1-1-11-11111-1-1-1-1111-1-11-1-1
χ61111111111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-11-11-111111-1-1-1-1-1-1-111-111
χ71111111111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-1-1-111111-1-1111-1-1
χ81111111111-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1-11111-111-1-1-111
χ911111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-11111-1-111-1-111-1-111-11-1-11-1
χ1011111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11-11111-1-111-1-1-1-11-111-11
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1111-11-11-11-1
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-111111-1-1-1-1-1-111-1-111-11-11-11-11
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1111-1-1-1-11111-1-11-1-11
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-111-1-11-111-111-1-1-1-111-1-111-111-1
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111-1-11-111-11-1-1-11111-1-11-111-1-1-11
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11-11-111-11-1-11111-1-1-11-1-1111-1
χ172222222222222222222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000202200020000000000-10000-1-1-1
χ182222222222222222222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-20-2-2000-2000000000010000111
χ19222222222222222222-12-1222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220200002000-1-1-1-1-1-1-1-100000000
χ20222222222222222222-12-1222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-20000-20001111111100000000
χ212222222222-2-2-2-222-2-22-12-1-1-1222222-1-1-1-1-1-11111-2-2-2-2-1-1-1-1111111110000202-2000-20000000000-10000-111
χ222222222222-2-2-2-222-2-22-12-1-1-1222222-1-1-1-1-1-11111-2-2-2-2-1-1-1-1111111110000-20-2200020000000000100001-1-1
χ232222222222-2-2-2-222-2-2-12-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-11111111122220-20000-2000-1-1-1-1111100000000
χ242222222222-2-2-2-222-2-2-12-1222-1-1-1-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-111111111-2-2-2-202000020001111-1-1-1-100000000
χ2522222-2-22222-222-2-2-2-22-12-1-1-122-2-2-2-2-1-1-1-111-1-11122-2-21111-1-1-1-11111000020-2-200020000000000-100001-11
χ2622222-2-22222-222-2-2-2-22-12-1-1-122-2-2-2-2-1-1-1-111-1-11122-2-21111-1-1-1-111110000-2022000-2000000000010000-11-1
χ2722222-2-22222-222-2-2-2-2-12-1222-1-11111-1-1-1-1-2-222-2-2-1-1111111-1-1-1-1111122-2-20-200002000-1-111-1-11100000000
χ2822222-2-22222-222-2-2-2-2-12-1222-1-11111-1-1-1-1-2-222-2-2-1-1111111-1-1-1-11111-2-222020000-200011-1-111-1-100000000
χ2922222-2-2222-22-2-2-2-2222-12-1-1-122-2-2-2-2-1-1-1-11111-1-1-2-22211111111-1-1-1-1000020-22000-20000000000-1000011-1
χ3022222-2-2222-22-2-2-2-2222-12-1-1-122-2-2-2-2-1-1-1-11111-1-1-2-22211111111-1-1-1-10000-202-20002000000000010000-1-11
χ3122222-2-2222-22-2-2-2-222-12-1222-1-11111-1-1-1-1-2-2-2-22211-1-111111111-1-1-1-122-2-2020000-2000-1-11111-1-100000000
χ3222222-2-2222-22-2-2-2-222-12-1222-1-11111-1-1-1-1-2-2-2-22211-1-111111111-1-1-1-1-2-2220-20000200011-1-1-1-11100000000
χ332-2-2222i−2i-22-200002i−2i0022-22-2-22-22i2i−2i−2i22-2-22i−2i000000002i2i−2i−2i000000002i−2i2-200000000002i−2i2-2000000000000
χ342-2-2222i−2i-22-200002i−2i0022-22-2-22-22i2i−2i−2i22-2-22i−2i000000002i2i−2i−2i00000000−2i2i-220000000000−2i2i-22000000000000
χ352-2-2222i−2i-22-200002i−2i00-1212-2-2-11−i−iii-1-1112i−2i00003−3−i3i3−i−iii33−3−3−i3−i3i3i32i−2i2-20000000000−ii-11−i3i33−300000000
χ362-2-2222i−2i-22-200002i−2i00-1212-2-2-11−i−iii-1-1112i−2i00003−3−i3i3−i−iii33−3−3−i3−i3i3i3−2i2i-220000000000i−i1-1i3−i3−3300000000
χ372-2-2222i−2i-22-200002i−2i00-1212-2-2-11−i−iii-1-1112i−2i0000−33i3−i3−i−iii−3−333i3i3−i3−i32i−2i2-20000000000−ii-11i3−i3−3300000000
χ382-2-2222i−2i-22-200002i−2i00-1212-2-2-11−i−iii-1-1112i−2i0000−33i3−i3−i−iii−3−333i3i3−i3−i3−2i2i-220000000000i−i1-1−i3i33−300000000
χ392-2-222−2i2i-22-20000−2i2i0022-22-2-22-2−2i−2i2i2i22-2-2−2i2i00000000−2i−2i2i2i000000002i−2i-2200000000002i−2i-22000000000000
χ402-2-222−2i2i-22-20000−2i2i0022-22-2-22-2−2i−2i2i2i22-2-2−2i2i00000000−2i−2i2i2i00000000−2i2i2-20000000000−2i2i2-2000000000000
χ412-2-222−2i2i-22-20000−2i2i00-1212-2-2-11ii−i−i-1-111−2i2i00003−3i3−i3ii−i−i33−3−3i3i3−i3−i32i−2i-220000000000−ii1-1−i3i3−3300000000
χ422-2-222−2i2i-22-20000−2i2i00-1212-2-2-11ii−i−i-1-111−2i2i00003−3i3−i3ii−i−i33−3−3i3i3−i3−i3−2i2i2-20000000000i−i-11i3−i33−300000000
χ432-2-222−2i2i-22-20000−2i2i00-1212-2-2-11ii−i−i-1-111−2i2i0000−33−i3i3ii−i−i−3−333−i3−i3i3i32i−2i-220000000000−ii1-1i3−i33−300000000
χ442-2-222−2i2i-22-20000−2i2i00-1212-2-2-11ii−i−i-1-111−2i2i0000−33−i3i3ii−i−i−3−333−i3−i3i3i3−2i2i2-20000000000i−i-11−i3i3−3300000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ464444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21111-2-2222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4744444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-22222111122-2-222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000
χ4844444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-2222211112222-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ4944-4-4400-4-4400000000444-44-4-4-400004-44-40000000000000000000000000000000000000000000000000000
χ5044-4-4400-4-44000000004-242-22-4-40000-22-220023−23000000000023−2323−230000000000000000000000000000000000
χ5144-4-4400-4-44000000004-242-22-4-40000-22-2200−23230000000000−2323−23230000000000000000000000000000000000
χ5244-4-4400-4-4400000000-24-2-44-422−2i32i3−2i32i3-22-220000000000−2i32i3−2i32i300000000000000000000000000000000000000
χ5344-4-4400-4-4400000000-24-2-44-4222i3−2i32i3−2i3-22-2200000000002i3−2i32i3−2i300000000000000000000000000000000000000
χ5444-4-4400-4-4400000000-2-2-22-2222−2i32i3−2i32i31-11-10023−23000000i3−i3i3−i3−33−333i−3i3i−3i000000000000000000000000000000
χ5544-4-4400-4-4400000000-2-2-22-2222−2i32i3−2i32i31-11-100−2323000000i3−i3i3−i33−33−3−3i3i−3i3i000000000000000000000000000000
χ5644-4-4400-4-4400000000-2-2-22-22222i3−2i32i3−2i31-11-10023−23000000−i3i3−i3i3−33−33−3i3i−3i3i000000000000000000000000000000
χ5744-4-4400-4-4400000000-2-2-22-22222i3−2i32i3−2i31-11-100−2323000000−i3i3−i3i33−33−33i−3i3i−3i000000000000000000000000000000
χ584-44-44004-4-40000000044-4-4-44-4400004-4-440000000000000000000000000000000000000000000000000000
χ594-44-44004-4-4000000004-2-422-2-440000-222-2000023−2300000000000023−23−2323000000000000000000000000000000
χ604-44-44004-4-4000000004-2-422-2-440000-222-20000−2323000000000000−232323−23000000000000000000000000000000
χ614-44-44004-4-400000000-242-4-442-223−23−2323-222-2000000000023−23−232300000000000000000000000000000000000000
χ624-44-44004-4-400000000-242-4-442-2−232323−23-222-20000000000−232323−2300000000000000000000000000000000000000
χ634-44-44004-4-400000000-2-2222-22-223−23−23231-1-11000023−230000−333−3-333-3−333−3000000000000000000000000000000
χ644-44-44004-4-400000000-2-2222-22-223−23−23231-1-110000−23230000−333−33-3-333−3−33000000000000000000000000000000
χ654-44-44004-4-400000000-2-2222-22-2−232323−231-1-11000023−2300003−3−333-3-33−333−3000000000000000000000000000000
χ664-44-44004-4-400000000-2-2222-22-2−232323−231-1-110000−232300003−3−33-333-33−3−33000000000000000000000000000000
χ674-4-4444i−4i-44-400004i−4i004-2-4-2224-44i4i−4i−4i-2-222−2i2i00000000−2i−2i2i2i00000000000000000000000000000000000000
χ684-4-4444i−4i-44-400004i−4i00-2-22-222-22−2i−2i2i2i11-1-1−2i2i000023−23−2i32i3ii−i−i−3−333i3i3−i3−i3000000000000000000000000000000
χ694-4-4444i−4i-44-400004i−4i00-2-22-222-22−2i−2i2i2i11-1-1−2i2i0000−23232i3−2i3ii−i−i33−3−3−i3−i3i3i3000000000000000000000000000000
χ704-4-444−4i4i-44-40000−4i4i004-2-4-2224-4−4i−4i4i4i-2-2222i−2i000000002i2i−2i−2i00000000000000000000000000000000000000
χ714-4-444−4i4i-44-40000−4i4i00-2-22-222-222i2i−2i−2i11-1-12i−2i000023−232i3−2i3−i−iii−3−333−i3−i3i3i3000000000000000000000000000000
χ724-4-444−4i4i-44-40000−4i4i00-2-22-222-222i2i−2i−2i11-1-12i−2i0000−2323−2i32i3−i−iii33−3−3i3i3−i3−i3000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000000220022000000000-1-1-1-1000
χ746666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000000-2-200-2-20000000001111000
χ756666-366-3-3-3-6-633-3-33300000000000000000000000000000000000000000000002-2002-2000000000-1-111000
χ766666-366-3-3-3-6-633-3-3330000000000000000000000000000000000000000000000-2200-2200000000011-1-1000
χ776666-3-6-6-3-3-36-6-3-3333300000000000000000000000000000000000000000000002200-2-2000000000-11-11000
χ786666-3-6-6-3-3-36-6-3-333330000000000000000000000000000000000000000000000-2-200220000000001-11-1000
χ796666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000000002-200-22000000000-111-1000
χ806666-3-6-6-3-3-3-663333-3-30000000000000000000000000000000000000000000000-22002-20000000001-1-11000
χ811212-12-12-60066-600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-60066-6000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-600-66600−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-600-666006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-612i−12i6-660000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-6−12i12i6-6600006i−6i0000000000000000000000000000000000000000000000000000000000000000000000

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