Finite Group Databasebeta

← Group #13147791

Character table — Group #13147791

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order122234466644121212121212336666661212121236661212121212121212121212121212121212121212121222442244444444666612121212612121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111-11-1-1-11-111-1-111-1-111-1-111-1-1
χ61111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-11-11-11-1111-1-111-1-1-1-111-1-111
χ71111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-111-1-11111-1-1-1-111
χ81111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1111-1-1-111-1-111-1-11111-1-1
χ911111-1-11111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-11111-1-1-111-1-1-1-1111-11-11-11-1
χ1011111-1-11111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1111111-1-1-1-111-11-11-11-11
χ1111111-1-11111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-111-1-11111-1-11-11-1-11-11
χ1211111-1-11111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-11-111-11-1-1-1-11111-1-1-11-111-11-1
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-11-111111-1-1-1-11-1-111-1-11
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-11-111-11-1-11-11111-1-1-1-1-111-1-111-1
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-11-1-1-11111-1-1-1-1-111111-1-11-111-1
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1-11-1-1-1-11111-111-11-1-11
χ172222222222222222222-12-1-122-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222000002000-1-1-1-1-1-1-1-100000000
χ182222222222222222222-12-1-122-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-200000-20001111111100000000
χ19222222222222222222-12-122-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000220022000000000000-1-1-1-1
χ20222222222222222222-12-122-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-200-2-20000000000001111
χ212222222222-2-222-2-2-2-22-12-1-122-1-1-1-1-1-1-1-1-1-2-2111122-2-2-1-1-1-1111111112222-200000-2000-1-111-1-11100000000
χ222222222222-2-222-2-2-2-22-12-1-122-1-1-1-1-1-1-1-1-1-2-2111122-2-2-1-1-1-111111111-2-2-2-2200000200011-1-111-1-100000000
χ232222222222-2-222-2-2-2-2-12-122-1-122222-1-1-1-111-2-2-2-2-1-111-1-1-1-111111111000000002-2002-2000000000000-1-111
χ242222222222-2-222-2-2-2-2-12-122-1-122222-1-1-1-111-2-2-2-2-1-111-1-1-1-11111111100000000-2200-2200000000000011-1-1
χ2522222-2-22222-2-2-222-2-22-12-1-122-11111-1-1-1-122-1-111-2-2-2-21111-1-1-1-1111122-2-2-2000002000-1-11111-1-100000000
χ2622222-2-22222-2-2-222-2-22-12-1-122-11111-1-1-1-122-1-111-2-2-2-21111-1-1-1-11111-2-222200000-200011-1-1-1-11100000000
χ2722222-2-22222-2-2-222-2-2-12-122-1-12-2-2-2-2-1-1-1-1-1-122-2-211111111-1-1-1-11111000000002200-2-2000000000000-11-11
χ2822222-2-22222-2-2-222-2-2-12-122-1-12-2-2-2-2-1-1-1-1-1-122-2-211111111-1-1-1-1111100000000-2-200220000000000001-11-1
χ2922222-2-2222-22-2-2-2-2222-12-1-122-11111-1-1-1-1-2-211-1-1-2-22211111111-1-1-1-122-2-2200000-2000-1-1-1-1111100000000
χ3022222-2-2222-22-2-2-2-2222-12-1-122-11111-1-1-1-1-2-211-1-1-2-22211111111-1-1-1-1-2-222-20000020001111-1-1-1-100000000
χ3122222-2-2222-22-2-2-2-222-12-122-1-12-2-2-2-2-1-1-1-111-2-22211-1-111111111-1-1-1-1000000002-200-22000000000000-111-1
χ3222222-2-2222-22-2-2-2-222-12-122-1-12-2-2-2-2-1-1-1-111-2-22211-1-111111111-1-1-1-100000000-22002-20000000000001-1-11
χ332-22-222i−2i2-2-2002i−2i000022-22-22-2-22i2i−2i−2i22-2-20000002i−2i002i2i−2i−2i000000002-22i−2i00000000002-2002i−2i0000000000
χ342-22-222i−2i2-2-2002i−2i000022-22-22-2-22i2i−2i−2i22-2-20000002i−2i002i2i−2i−2i00000000-22−2i2i0000000000-2200−2i2i0000000000
χ352-22-222i−2i2-2-2002i−2i00002-1-2-112-21−i−iii-1-111003−3−i3i32i−2i00−i−iii33−3−3−i3−i3i3i32-22i−2i0000000000-11−i3i3−ii3−300000000
χ362-22-222i−2i2-2-2002i−2i00002-1-2-112-21−i−iii-1-111003−3−i3i32i−2i00−i−iii33−3−3−i3−i3i3i3-22−2i2i00000000001-1i3−i3i−i−3300000000
χ372-22-222i−2i2-2-2002i−2i00002-1-2-112-21−i−iii-1-11100−33i3−i32i−2i00−i−iii−3−333i3i3−i3−i32-22i−2i0000000000-11i3−i3−ii−3300000000
χ382-22-222i−2i2-2-2002i−2i00002-1-2-112-21−i−iii-1-11100−33i3−i32i−2i00−i−iii−3−333i3i3−i3−i3-22−2i2i00000000001-1−i3i3i−i3−300000000
χ392-22-22−2i2i2-2-200−2i2i000022-22-22-2-2−2i−2i2i2i22-2-2000000−2i2i00−2i−2i2i2i000000002-2−2i2i00000000002-200−2i2i0000000000
χ402-22-22−2i2i2-2-200−2i2i000022-22-22-2-2−2i−2i2i2i22-2-2000000−2i2i00−2i−2i2i2i00000000-222i−2i0000000000-22002i−2i0000000000
χ412-22-22−2i2i2-2-200−2i2i00002-1-2-112-21ii−i−i-1-111003−3i3−i3−2i2i00ii−i−i33−3−3i3i3−i3−i32-2−2i2i0000000000-11i3−i3i−i3−300000000
χ422-22-22−2i2i2-2-200−2i2i00002-1-2-112-21ii−i−i-1-111003−3i3−i3−2i2i00ii−i−i33−3−3i3i3−i3−i3-222i−2i00000000001-1−i3i3−ii−3300000000
χ432-22-22−2i2i2-2-200−2i2i00002-1-2-112-21ii−i−i-1-11100−33−i3i3−2i2i00ii−i−i−3−333−i3−i3i3i32-2−2i2i0000000000-11−i3i3i−i−3300000000
χ442-22-22−2i2i2-2-200−2i2i00002-1-2-112-21ii−i−i-1-11100−33−i3i3−2i2i00ii−i−i−3−333−i3−i3i3i3-222i−2i00000000001-1i3−i3−ii3−300000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21111222222-2-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4744444-4-44444-4-4-444-4-4-2-2-2-2-2-2-2-222221111-2-2-2-2222222-1-1-1-11111-1-1-1-1000000000000000000000000000000
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
χ4944-4-4400-44-400000000444-44-4-4-400004-44-40000000000000000000000000000000000000000000000000000
χ5044-4-4400-44-4000000004-242-2-4-4223−2323−23-22-22000000000023−2323−2300000000000000000000000000000000000000
χ5144-4-4400-44-4000000004-242-2-4-42−2323−2323-22-220000000000−2323−232300000000000000000000000000000000000000
χ5244-4-4400-44-400000000-24-2-4422-40000-22-22−2i32i3000000000000−2i32i3−2i32i30000000000000000000000000000000000
χ5344-4-4400-44-400000000-24-2-4422-40000-22-222i3−2i30000000000002i3−2i32i3−2i30000000000000000000000000000000000
χ5444-4-4400-44-400000000-2-2-22-222223−2323−231-11-1−2i32i300000000−33−33i3−i3i3−i33i−3i3i−3i000000000000000000000000000000
χ5544-4-4400-44-400000000-2-2-22-222223−2323−231-11-12i3−2i300000000−33−33−i3i3−i3i3−3i3i−3i3i000000000000000000000000000000
χ5644-4-4400-44-400000000-2-2-22-2222−2323−23231-11-1−2i32i3000000003−33−3i3−i3i3−i3−3i3i−3i3i000000000000000000000000000000
χ5744-4-4400-44-400000000-2-2-22-2222−2323−23231-11-12i3−2i3000000003−33−3−i3i3−i3i33i−3i3i−3i000000000000000000000000000000
χ584-44-444i−4i4-4-4004i−4i0000-2424-4-22-44i4i−4i−4i-2-222000000−2i2i00−2i−2i2i2i00000000000000000000000000000000000000
χ594-44-444i−4i4-4-4004i−4i0000-2-22-22-222−2i−2i2i2i11-1-10023−23−2i32i3−2i2i00ii−i−i−3−333i3i3−i3−i3000000000000000000000000000000
χ604-44-444i−4i4-4-4004i−4i0000-2-22-22-222−2i−2i2i2i11-1-100−23232i3−2i3−2i2i00ii−i−i33−3−3−i3−i3i3i3000000000000000000000000000000
χ614-44-44−4i4i4-4-400−4i4i0000-2424-4-22-4−4i−4i4i4i-2-2220000002i−2i002i2i−2i−2i00000000000000000000000000000000000000
χ624-44-44−4i4i4-4-400−4i4i0000-2-22-22-2222i2i−2i−2i11-1-10023−232i3−2i32i−2i00−i−iii−3−333−i3−i3i3i3000000000000000000000000000000
χ634-44-44−4i4i4-4-400−4i4i0000-2-22-22-2222i2i−2i−2i11-1-100−2323−2i32i32i−2i00−i−iii33−3−3i3i3−i3−i3000000000000000000000000000000
χ644-4-44400-4-440000000044-4-4-4-44400004-4-440000000000000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-422-44-2−2i32i32i3−2i3-222-20000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ664-4-44400-4-44000000004-2-422-44-22i3−2i3−2i32i3-222-200000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ674-4-44400-4-4400000000-242-4-42-240000-222-20000000023−230000000023−23−2323000000000000000000000000000000
χ684-4-44400-4-4400000000-242-4-42-240000-222-200000000−232300000000−232323−23000000000000000000000000000000
χ694-4-44400-4-4400000000-2-22222-2-2−2i32i32i3−2i31-1-110000000023−23i3−i3−i3i3−3i3i3i−3i−333−3000000000000000000000000000000
χ704-4-44400-4-4400000000-2-22222-2-2−2i32i32i3−2i31-1-1100000000−2323i3−i3−i3i33i−3i−3i3i3−3−33000000000000000000000000000000
χ714-4-44400-4-4400000000-2-22222-2-22i3−2i3−2i32i31-1-110000000023−23−i3i3i3−i33i−3i−3i3i−333−3000000000000000000000000000000
χ724-4-44400-4-4400000000-2-22222-2-22i3−2i3−2i32i31-1-1100000000−2323−i3i3i3−i3−3i3i3i−3i3−3−33000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000022200020000000000-1-1-1-10000
χ746666-366-3-3-366-3-3-3-3-3-30000000000000000000000000000000000000000000-2-2-2000-2000000000011110000
χ756666-366-3-3-3-6-6-3-33333000000000000000000000000000000000000000000022-2000-20000000000-1-1110000
χ766666-366-3-3-3-6-6-3-333330000000000000000000000000000000000000000000-2-220002000000000011-1-10000
χ776666-3-6-6-3-3-36-633-3-33300000000000000000000000000000000000000000002-22000-20000000000-11-110000
χ786666-3-6-6-3-3-36-633-3-3330000000000000000000000000000000000000000000-22-2000200000000001-11-10000
χ796666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000002-2-200020000000000-111-10000
χ806666-3-6-6-3-3-3-663333-3-30000000000000000000000000000000000000000000-222000-200000000001-1-110000
χ811212-12-12-6006-6600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6006-66000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-612i−12i-66600−6i6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-6−12i12i-666006i−6i000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-6000063−630000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-60000−63630000000000000000000000000000000000000000000000000000000000000000000000

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