Finite Group Databasebeta

← Group #13150665

Character table — Group #13150665

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466612121212266121233666666121212123666666666661212121212121212121212121212444444442444444466121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1111111-1-11-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-11111-1-111-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-111-1-11-11111-1-111-1-1-1-111-1-1-1-11111-1-111
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-11111-1-1-1-1-1-1111111-1-1
χ911111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-11111-1-11-11-11-1-1-111-1-11111-1-111-1-11-11-1
χ1011111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-111-1-1111-1-111-1-111-1-111-1-1-11-11
χ1111111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1111111-1-1-11-11-11-1-111-1-111-1-111-1-111-11-11
χ1211111-1-111111-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111-1-111-111-1-111-1-1-1-111-1-1111-11-1
χ1311111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-11-111-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-1-11-111111-1-1-1-111-1-1-1-111-111-1
χ1511111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-11-1-11-1-1-1-11111-1-11111-1-1-111-1
χ1611111-1-1-1-1111-1-1-1-1111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-11-11111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222222222-12-12-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200000000220000000000-1-1-1-1-1-1-1-10000
χ182222222222222222222222-12-12-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000000000111111110000
χ19222222222222222222222-12-12-122-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000002200220000000000000000-1-1-1-1
χ20222222222222222222222-12-12-122-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-200-2-200000000000000001111
χ212222222-2-22222222-2-2-2-2-22-12-12-1-121111-1-2-211-1-11111-1-1-122-2-2-1-1-1-11111222200000000-2-20000000000-1-1-1-111110000
χ222222222-2-22222222-2-2-2-2-22-12-12-1-121111-1-2-211-1-11111-1-1-122-2-2-1-1-1-11111-2-2-2-2000000002200000000001111-1-1-1-10000
χ232222222-2-22222222-2-2-2-2-2-12-12-122-1-2-2-2-2-111-2-2-1-11111-122-1-111-1-1-1-1111100000000002200-2-2000000000000000011-1-1
χ242222222-2-22222222-2-2-2-2-2-12-12-122-1-2-2-2-2-111-2-2-1-11111-122-1-111-1-1-1-111110000000000-2-200220000000000000000-1-111
χ2522222-2-222222-2-2-2-2-2-2-2222-12-12-1-12-1-1-1-1-1-2-211-1-11111-111-2-2221111-1-1-1-122-2-2000000002-20000000000-1-111-1-1110000
χ2622222-2-222222-2-2-2-2-2-2-2222-12-12-1-12-1-1-1-1-1-2-211-1-11111-111-2-2221111-1-1-1-1-2-22200000000-22000000000011-1-111-1-10000
χ2722222-2-222222-2-2-2-2-2-2-222-12-12-122-12222-111-2-2-1-11111-1-2-211-1-11111-1-1-1-100000000002-2002-20000000000000000-11-11
χ2822222-2-222222-2-2-2-2-2-2-222-12-12-122-12222-111-2-2-1-11111-1-2-211-1-11111-1-1-1-10000000000-2200-2200000000000000001-11-1
χ2922222-2-2-2-2222-2-2-2-2222-2-22-12-12-1-121111-122-1-1-1-1-1-1-1-1-111-2-2-2-21111111122-2-200000000-220000000000-1-11111-1-10000
χ3022222-2-2-2-2222-2-2-2-2222-2-22-12-12-1-121111-122-1-1-1-1-1-1-1-1-111-2-2-2-211111111-2-222000000002-2000000000011-1-1-1-1110000
χ3122222-2-2-2-2222-2-2-2-2222-2-2-12-12-122-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-211111111111100000000002-200-2200000000000000001-1-11
χ3222222-2-2-2-2222-2-2-2-2222-2-2-12-12-122-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-21111111111110000000000-22002-20000000000000000-111-1
χ332-22-222-200-2-2222-2-20000022-22-2-2-22000020000-2-2000022-22-20022-2-200002i−2i2i−2i000000000000000000002i−2i2i−2i00000000
χ342-22-222-200-2-2222-2-20000022-22-2-2-22000020000-2-2000022-22-20022-2-20000−2i2i−2i2i00000000000000000000−2i2i−2i2i00000000
χ352-22-222-200-2-2222-2-2000002-1-2-1-2112−i3−i3i3i3-100−i3i311−i3−i3i3i3-1-112-200-1-111−i3−i3i3i32i−2i2i−2i00000000000000000000−ii−ii3−33−30000
χ362-22-222-200-2-2222-2-2000002-1-2-1-2112−i3−i3i3i3-100−i3i311−i3−i3i3i3-1-112-200-1-111−i3−i3i3i3−2i2i−2i2i00000000000000000000i−ii−i−33−330000
χ372-22-222-200-2-2222-2-2000002-1-2-1-2112i3i3−i3−i3-100i3−i311i3i3−i3−i3-1-112-200-1-111i3i3−i3−i32i−2i2i−2i00000000000000000000−ii−ii−33−330000
χ382-22-222-200-2-2222-2-2000002-1-2-1-2112i3i3−i3−i3-100i3−i311i3i3−i3−i3-1-112-200-1-111i3i3−i3−i3−2i2i−2i2i00000000000000000000i−ii−i3−33−30000
χ392-22-22-2200-2-22-2-2220000022-22-2-2-22000020000-2-200002-22-2200-2-22200002i−2i−2i2i000000000000000000002i−2i−2i2i00000000
χ402-22-22-2200-2-22-2-2220000022-22-2-2-22000020000-2-200002-22-2200-2-2220000−2i2i2i−2i00000000000000000000−2i2i2i−2i00000000
χ412-22-22-2200-2-22-2-222000002-1-2-1-2112−i3−i3i3i3-100i3−i311i3i3−i3−i3-11-1-220011-1-1−i3−i3i3i32i−2i−2i2i00000000000000000000−iii−i3−3−330000
χ422-22-22-2200-2-22-2-222000002-1-2-1-2112−i3−i3i3i3-100i3−i311i3i3−i3−i3-11-1-220011-1-1−i3−i3i3i3−2i2i2i−2i00000000000000000000i−i−ii−333−30000
χ432-22-22-2200-2-22-2-222000002-1-2-1-2112i3i3−i3−i3-100−i3i311−i3−i3i3i3-11-1-220011-1-1i3i3−i3−i32i−2i−2i2i00000000000000000000−iii−i−333−30000
χ442-22-22-2200-2-22-2-222000002-1-2-1-2112i3i3−i3−i3-100−i3i311−i3−i3i3i3-11-1-220011-1-1i3i3−i3−i3−2i2i2i−2i00000000000000000000i−i−ii3−3−330000
χ452-2-222002i−2i2-2-200000002i−2i22-2-222-2-22i−2i2i−2i200002-20000-200002i−2i00002i−2i2i−2i00002i−2i2-200000000002-2002i−2i000000000000
χ462-2-222002i−2i2-2-200000002i−2i22-2-222-2-22i−2i2i−2i200002-20000-200002i−2i00002i−2i2i−2i0000−2i2i-220000000000-2200−2i2i000000000000
χ472-2-22200−2i2i2-2-20000000−2i2i22-2-222-2-2−2i2i−2i2i200002-20000-20000−2i2i0000−2i2i−2i2i00002i−2i-220000000000-22002i−2i000000000000
χ482-2-22200−2i2i2-2-20000000−2i2i22-2-222-2-2−2i2i−2i2i200002-20000-20000−2i2i0000−2i2i−2i2i0000−2i2i2-200000000002-200−2i2i000000000000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-2-2-2221111-1-1-1-1000000000000000000000000000000000000
χ5144444-4-444444-4-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-112222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-4444-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5344-4-440000-44-4000000000444-4-4-44-4000040000-440000-400000000000000000000000000000000000000000000000000
χ5444-4-440000-44-40000000004-242-42-2-423−23−2323-200002-200002000000000023−23−2323000000000000000000000000000000000000
χ5544-4-440000-44-40000000004-242-42-2-4−232323−23-200002-2000020000000000−232323−23000000000000000000000000000000000000
χ5644-4-440000-44-4000000000-24-2-42-4420000-2−2i32i3002-2−2i32i3−2i32i3200000000000000000000000000000000000000000000000000
χ5744-4-440000-44-4000000000-24-2-42-4420000-22i3−2i3002-22i3−2i32i3−2i3200000000000000000000000000000000000000000000000000
χ5844-4-440000-44-4000000000-2-2-2222-2223−23−23231−2i32i300-11i3−i3i3−i3-10000003i−3i3i−3i−333−3000000000000000000000000000000000000
χ5944-4-440000-44-4000000000-2-2-2222-2223−23−232312i3−2i300-11−i3i3−i3i3-1000000−3i3i−3i3i−333−3000000000000000000000000000000000000
χ6044-4-440000-44-4000000000-2-2-2222-22−232323−231−2i32i300-11i3−i3i3−i3-1000000−3i3i−3i3i3−3−33000000000000000000000000000000000000
χ6144-4-440000-44-4000000000-2-2-2222-22−232323−2312i3−2i300-11−i3i3−i3i3-10000003i−3i3i−3i3−3−33000000000000000000000000000000000000
χ624-44-444-400-4-4444-4-400000-24242-4-4-20000-20000220000-24-4-2200-2-2220000000000000000000000000000000000000000
χ634-44-444-400-4-4444-4-400000-2-22-2222-2−2i3−2i32i32i3100−2i32i3-1-1i3i3−i3−i31-22-220011-1-1i3i3−i3−i3000000000000000000000000000000000000
χ644-44-444-400-4-4444-4-400000-2-22-2222-22i32i3−2i3−2i31002i3−2i3-1-1−i3−i3i3i31-22-220011-1-1−i3−i3i3i3000000000000000000000000000000000000
χ654-44-44-4400-4-44-4-44400000-24242-4-4-20000-20000220000-2-442-20022-2-20000000000000000000000000000000000000000
χ664-44-44-4400-4-44-4-44400000-2-22-2222-2−2i3−2i32i32i31002i3−2i3-1-1−i3−i3i3i312-22-200-1-111i3i3−i3−i3000000000000000000000000000000000000
χ674-44-44-4400-4-44-4-44400000-2-22-2222-22i32i3−2i3−2i3100−2i32i3-1-1i3i3−i3−i312-22-200-1-111−i3−i3i3i3000000000000000000000000000000000000
χ684-4-444004i−4i4-4-400000004i−4i4-2-424-22-4−2i2i−2i2i-20000-220000200004i−4i0000−2i2i−2i2i000000000000000000000000000000000000
χ694-4-444004i−4i4-4-400000004i−4i-242-4-24-424i−4i4i−4i-20000-22000020000−2i2i0000−2i2i−2i2i000000000000000000000000000000000000
χ704-4-444004i−4i4-4-400000004i−4i-2-222-2-222−2i2i−2i2i100001-13-3-33-10000−2i2i−3i3i3i−3ii−ii−i000000000000000000000000000000000000
χ714-4-444004i−4i4-4-400000004i−4i-2-222-2-222−2i2i−2i2i100001-1-333-3-10000−2i2i3i−3i−3i3ii−ii−i000000000000000000000000000000000000
χ724-4-44400−4i4i4-4-40000000−4i4i4-2-424-22-42i−2i2i−2i-20000-22000020000−4i4i00002i−2i2i−2i000000000000000000000000000000000000
χ734-4-44400−4i4i4-4-40000000−4i4i-242-4-24-42−4i4i−4i4i-20000-220000200002i−2i00002i−2i2i−2i000000000000000000000000000000000000
χ744-4-44400−4i4i4-4-40000000−4i4i-2-222-2-2222i−2i2i−2i100001-13-3-33-100002i−2i3i−3i−3i3i−ii−ii000000000000000000000000000000000000
χ754-4-44400−4i4i4-4-40000000−4i4i-2-222-2-2222i−2i2i−2i100001-1-333-3-100002i−2i−3i3i3i−3i−ii−ii000000000000000000000000000000000000
χ766666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222222000000-1-1-1-1-1-1-1-1000000000000
χ776666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-2-2-200000011111111000000000000
χ786666-366-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-22-2000000-1-11111-1-1000000000000
χ796666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222-2200000011-1-1-1-111000000000000
χ806666-3-6-666-3-3-33333-633-3-30000000000000000000000000000000000000000002222-2-200000011-1-111-1-1000000000000
χ816666-3-6-666-3-3-33333-633-3-3000000000000000000000000000000000000000000-2-2-2-222000000-1-111-1-111000000000000
χ826666-3-6-6-6-6-3-3-333336-3-33300000000000000000000000000000000000000000022-2-2-220000001111-1-1-1-1000000000000
χ836666-3-6-6-6-6-3-3-333336-3-333000000000000000000000000000000000000000000-2-2222-2000000-1-1-1-11111000000000000
χ846-6-66-3006i−6i-33333−3333−330−3i33i3−3i3i0000000000000000000000000000000000000000002i−2i2-200000000−i3i3-113−3−ii000000000000
χ856-6-66-3006i−6i-33333−3333−330−3i33i3−3i3i000000000000000000000000000000000000000000−2i2i-2200000000i3−i31-1−33i−i000000000000
χ866-6-66-3006i−6i-333−3333−333303i3−3i3−3i3i0000000000000000000000000000000000000000002i−2i2-200000000i3−i3-11−33−ii000000000000
χ876-6-66-3006i−6i-333−3333−333303i3−3i3−3i3i000000000000000000000000000000000000000000−2i2i-2200000000−i3i31-13−3i−i000000000000
χ886-6-66-300−6i6i-33333−3333−3303i3−3i33i−3i0000000000000000000000000000000000000000002i−2i-2200000000−i3i31-1−33−ii000000000000
χ896-6-66-300−6i6i-33333−3333−3303i3−3i33i−3i000000000000000000000000000000000000000000−2i2i2-200000000i3−i3-113−3i−i000000000000
χ906-6-66-300−6i6i-333−3333−33330−3i33i33i−3i0000000000000000000000000000000000000000002i−2i-2200000000i3−i31-13−3−ii000000000000
χ916-6-66-300−6i6i-333−3333−33330−3i33i33i−3i000000000000000000000000000000000000000000−2i2i2-200000000−i3i3-11−33i−i000000000000
χ921212-12-12-600006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-12-600006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-1212-12-612-120066-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-1212-12-6-12120066-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000

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