Finite Group Databasebeta

← Group #13150715

Character table — Group #13150715

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666246612121212336666661212121236666666666612121212121212121212121212122244244444444466121212121212612121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-11-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-11111-1-1-1
χ51111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111111-11-1-11-1-11-111-1-1-1-11111-11-11-1-1
χ61111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1111-1-1-1-111-1-11-11-111
χ71111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11-1-11111-1-11-11-111-1-1
χ81111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-111-1-1-11111-1-1-11-11-1-111
χ911111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11-11-111111-1-1-1-111-1-11-1-11
χ1011111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-11-11111-1-1-1-1-1-111-111-1
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-111-1-1-11
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-11-1-1-1-11111-11-1-1111-1
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-111-1-1111-1-1-111-1-111-1-1111-1-1-11-1
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-111-1-1-1-111111-1-111-1-1-1-1-1111-11
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1111-1-111-1-1-111-1-111-1-1111-1-111-11-1
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-1-111-1111-1-1-1-111-1-111-111-1-11-11
χ172222222222222222222-122-1-12-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000202020020000000000-10000-1-1-1
χ182222222222222222222-122-1-12-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-20-20-200-2000000000010000111
χ19222222222222222222-12-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220202000000-1-1-1-1-1-1-1-100000000
χ20222222222222222222-12-1-122-12-1-1-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20-20-20000001111111100000000
χ212222222222-2-2-2-222-2-22-122-1-12-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-1111100002020-200-20000000000-10000-111
χ222222222222-2-2-2-222-2-22-122-1-12-12222-1-2-211-1-11111-1-1-1-2-211-1-1-1-111110000-20-2020020000000000100001-1-1
χ232222222222-2-2-2-222-2-2-12-1-122-12-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-1111122220-20-2000000-1-11111-1-100000000
χ242222222222-2-2-2-222-2-2-12-1-122-12-1-1-1-1-111-2-2-1-11111-12211-2-2-1-1-1-11111-2-2-2-2020200000011-1-1-1-11100000000
χ2522222-2-22222-222-2-2-2-22-122-1-12-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-21111111111000020-20-20020000000000-1000011-1
χ2622222-2-22222-222-2-2-2-22-122-1-12-1-2-2-2-2-122-1-1-1-1-1-1-1-1-111-2-211111111110000-2020200-2000000000010000-1-11
χ2722222-2-22222-222-2-2-2-2-12-1-122-121111-1-1-122-1-1-1-1-1-1-1-2-211-2-21111111122-2-20-202000000-1-1-1-1111100000000
χ2822222-2-22222-222-2-2-2-2-12-1-122-121111-1-1-122-1-1-1-1-1-1-1-2-211-2-211111111-2-222020-20000001111-1-1-1-100000000
χ2922222-2-2222-22-2-2-2-2222-122-1-12-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-1000020-20200-20000000000-100001-11
χ3022222-2-2222-22-2-2-2-2222-122-1-12-1-2-2-2-2-1-2-211-1-11111-11122-1-11111-1-1-1-10000-2020-2002000000000010000-11-1
χ3122222-2-2222-22-2-2-2-222-12-1-122-121111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-122-2-2020-2000000-1-111-1-11100000000
χ3222222-2-2222-22-2-2-2-222-12-1-122-121111-111-2-2-1-11111-1-2-2-1-1221111-1-1-1-1-2-2220-20200000011-1-111-1-100000000
χ332-22-222i−2i-22-200002i−2i00222-22-2-2-22i2i−2i−2i200002-20000-22i−2i00002i2i−2i−2i00002-22i−2i00000000002-200002i−2i00000000
χ342-22-222i−2i-22-200002i−2i00222-22-2-2-22i2i−2i−2i200002-20000-22i−2i00002i2i−2i−2i0000-22−2i2i0000000000-220000−2i2i00000000
χ352-22-222i−2i-22-200002i−2i00-12-112-21-2−i−iii-1−i3i300-11−i3−i3i3i312i−2i3−300−i−iii33−3−32-22i−2i0000000000-11−i3i33−3−ii00000000
χ362-22-222i−2i-22-200002i−2i00-12-112-21-2−i−iii-1−i3i300-11−i3−i3i3i312i−2i3−300−i−iii33−3−3-22−2i2i00000000001-1i3−i3−33i−i00000000
χ372-22-222i−2i-22-200002i−2i00-12-112-21-2−i−iii-1i3−i300-11i3i3−i3−i312i−2i−3300−i−iii−3−3332-22i−2i0000000000-11i3−i3−33−ii00000000
χ382-22-222i−2i-22-200002i−2i00-12-112-21-2−i−iii-1i3−i300-11i3i3−i3−i312i−2i−3300−i−iii−3−333-22−2i2i00000000001-1−i3i33−3i−i00000000
χ392-22-22−2i2i-22-20000−2i2i00222-22-2-2-2−2i−2i2i2i200002-20000-2−2i2i0000−2i−2i2i2i00002-2−2i2i00000000002-20000−2i2i00000000
χ402-22-22−2i2i-22-20000−2i2i00222-22-2-2-2−2i−2i2i2i200002-20000-2−2i2i0000−2i−2i2i2i0000-222i−2i0000000000-2200002i−2i00000000
χ412-22-22−2i2i-22-20000−2i2i00-12-112-21-2ii−i−i-1−i3i300-11−i3−i3i3i31−2i2i−3300ii−i−i−3−3332-2−2i2i0000000000-11−i3i3−33i−i00000000
χ422-22-22−2i2i-22-20000−2i2i00-12-112-21-2ii−i−i-1−i3i300-11−i3−i3i3i31−2i2i−3300ii−i−i−3−333-222i−2i00000000001-1i3−i33−3−ii00000000
χ432-22-22−2i2i-22-20000−2i2i00-12-112-21-2ii−i−i-1i3−i300-11i3i3−i3−i31−2i2i3−300ii−i−i33−3−32-2−2i2i0000000000-11i3−i33−3i−i00000000
χ442-22-22−2i2i-22-20000−2i2i00-12-112-21-2ii−i−i-1i3−i300-11i3i3−i3−i31−2i2i3−300ii−i−i33−3−3-222i−2i00000000001-1−i3i3−33−ii00000000
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
χ4944-4-44004-4-40000000044-44-44-4-4000040000-440000-400000000000000000000000000000000000000000000
χ5044-4-44004-4-4000000004-2-442-2-420000-200002-200002000023−23000023−2323−23000000000000000000000000000000
χ5144-4-44004-4-4000000004-2-442-2-420000-200002-2000020000−23230000−2323−2323000000000000000000000000000000
χ5244-4-44004-4-400000000-242-2-442-423−2323−23-200002-20000200000023−2323−230000000000000000000000000000000000
χ5344-4-44004-4-400000000-242-2-442-4−2323−2323-200002-200002000000−2323−23230000000000000000000000000000000000
χ5444-4-44004-4-400000000-2-22-22-22223−2323−2310000-113-33-3-1000023−23−33−33−33−33000000000000000000000000000000
χ5544-4-44004-4-400000000-2-22-22-22223−2323−2310000-11-33-33-10000−2323−33−333−33−3000000000000000000000000000000
χ5644-4-44004-4-400000000-2-22-22-222−2323−232310000-113-33-3-10000−23233−33−33−33−3000000000000000000000000000000
χ5744-4-44004-4-400000000-2-22-22-222−2323−232310000-11-33-33-1000023−233−33−3−33−33000000000000000000000000000000
χ584-44-444i−4i-44-400004i−4i004-24-4-22-424i4i−4i−4i-20000-2200002−2i2i0000−2i−2i2i2i0000000000000000000000000000000000
χ594-44-444i−4i-44-400004i−4i00-2-2-22-2222−2i−2i2i2i1−2i32i3001-1i3i3−i3−i3-1−2i2i23−2300ii−i−i−3−333000000000000000000000000000000
χ604-44-444i−4i-44-400004i−4i00-2-2-22-2222−2i−2i2i2i12i3−2i3001-1−i3−i3i3i3-1−2i2i−232300ii−i−i33−3−3000000000000000000000000000000
χ614-44-44−4i4i-44-40000−4i4i004-24-4-22-42−4i−4i4i4i-20000-22000022i−2i00002i2i−2i−2i0000000000000000000000000000000000
χ624-44-44−4i4i-44-40000−4i4i00-2-2-22-22222i2i−2i−2i1−2i32i3001-1i3i3−i3−i3-12i−2i−232300−i−iii33−3−3000000000000000000000000000000
χ634-44-44−4i4i-44-40000−4i4i00-2-2-22-22222i2i−2i−2i12i3−2i3001-1−i3−i3i3i3-12i−2i23−2300−i−iii−3−333000000000000000000000000000000
χ644-4-44400-4-440000000044-4-4-4-444000040000-4-40000400000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-4-4224-20000-200−2i32i322−2i32i32i3−2i3-200000000000000000000000000000000000000000000
χ664-4-44400-4-44000000004-2-4-4224-20000-2002i3−2i3222i3−2i3−2i32i3-200000000000000000000000000000000000000000000
χ674-4-44400-4-4400000000-2422-4-4-24−2i32i32i3−2i3-20000220000-2000000−2i32i32i3−2i30000000000000000000000000000000000
χ684-4-44400-4-4400000000-2422-4-4-242i3−2i3−2i32i3-20000220000-20000002i3−2i3−2i32i30000000000000000000000000000000000
χ694-4-44400-4-4400000000-2-22222-2-2−2i32i32i3−2i3100−2i32i3-1-1i3−i3−i3i31000000i3−i3−i3i33-3-33000000000000000000000000000000
χ704-4-44400-4-4400000000-2-22222-2-2−2i32i32i3−2i31002i3−2i3-1-1−i3i3i3−i31000000i3−i3−i3i3-333-3000000000000000000000000000000
χ714-4-44400-4-4400000000-2-22222-2-22i3−2i3−2i32i3100−2i32i3-1-1i3−i3−i3i31000000−i3i3i3−i3-333-3000000000000000000000000000000
χ724-4-44400-4-4400000000-2-22222-2-22i3−2i3−2i32i31002i3−2i3-1-1−i3i3i3−i31000000−i3i3i3−i33-3-33000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000000022022000000000-1-1-1-1000
χ746666-366-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000000-2-20-2-20000000001111000
χ756666-366-3-3-3-6-633-3-333000000000000000000000000000000000000000000000002-202-2000000000-11-11000
χ766666-366-3-3-3-6-633-3-33300000000000000000000000000000000000000000000000-220-220000000001-11-1000
χ776666-3-6-6-3-3-36-6-3-33333000000000000000000000000000000000000000000000002-20-22000000000-111-1000
χ786666-3-6-6-3-3-36-6-3-3333300000000000000000000000000000000000000000000000-2202-20000000001-1-11000
χ796666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000000000220-2-2000000000-1-111000
χ806666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000000000-2-202200000000011-1-1000
χ811212-12-12-600-66600−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-600-666006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-612i−12i6-660000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-6−12i12i6-6600006i−6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-6000000−6i36i300000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-60000006i3−6i300000000000000000000000000000000000000000000000000000000000000000000

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