Finite Group Databasebeta

← Group #13151335

Character table — Group #13151335

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1222344666226666121233666666444436661212121222444444441212121266666666121222444466121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ51111111111-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ61111111111-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1
χ81111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111
χ911111-1-11111-111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111111-11-111-1-1-1-11-11-11-111-1-111-1-111-1-1-1-11-11-1
χ1011111-1-11111-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-111111-11-111-1-1-1-1-111-1-11-1-1-1-111-1-1-1-11111-11-11
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11-11-111-1-1-1-1-11-111-11111-1-111-1-111-1-1-111-1
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11-11-111-1-1-1-11-1-11-11-1-111-1-11111-1-1111-1-11
χ1311111-1-1111-11-1-111-1-11111111111111111-1-1-1-111-1-1-1-1-1-1111111-11-11-1-111-1-1-11-11-1111-1-1-1-11111-1-1-1-1-11-11
χ1411111-1-1111-11-1-111-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-11-11-1-111-1-11-1-111-1-1-1-1-1-1-111-1-111111-11-1
χ1511111-1-1111-11-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-11-11-1-111-1-11-11-1-11111111-1-1-1-111-1-11-1-11
χ1611111-1-1111-11-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-11-11-1-111-1-1-111-11-1-1-11111-1-111-1-111-111-1
χ172222222222222222222-12-1-1-1220000-1-1-1-1-1-1220000002222000022-1-1-1-1-1-1-1-122000000000000-1-1-1-100-1-100
χ182222222222222222222-12-1-1-1220000-1-1-1-1-1-122000000-2-2-2-2000022-1-1-1-1-1-1-1-1-2-20000000000001111001100
χ19222222222222222222-12-1222-1-10000-1-1-1-122-1-122220000000000-1-122-1-1-1-1-1-1000022-1-10000000000-1-100-1-1
χ20222222222222222222-12-1222-1-10000-1-1-1-122-1-1-2-2-2-20000000000-1-122-1-1-1-1-1-10000-2-2110000000000110011
χ212222222222-2-2-2-2-2-2222-12-1-1-1220000-1-1-1-1-1-12200000022220000-2-2111111-1-1-2-2000000000000-1-1-1-1001100
χ222222222222-2-2-2-2-2-2222-12-1-1-1220000-1-1-1-1-1-122000000-2-2-2-20000-2-2111111-1-122000000000000111100-1-100
χ232222222222-2-2-2-2-2-222-12-1222-1-10000-1-1-1-122-1-12222000000000011-2-21111-1-10000-2-2-1-10000000000-1-10011
χ242222222222-2-2-2-2-2-222-12-1222-1-10000-1-1-1-122-1-1-2-2-2-2000000000011-2-21111-1-10000221100000000001100-1-1
χ2522222-2-22222-222-2-2-2-22-12-1-1-1220000-1-1-1-111-2-200000022-2-200002-2-11-1-11111-2200000000000011-1-1001-100
χ2622222-2-22222-222-2-2-2-22-12-1-1-1220000-1-1-1-111-2-2000000-2-22200002-2-11-1-111112-2000000000000-1-11100-1100
χ2722222-2-22222-222-2-2-2-2-12-1222-1-10000-1-1-1-1-2-21122-2-20000000000-112-2-1-1111100002-2-1-100000000001100-11
χ2822222-2-22222-222-2-2-2-2-12-1222-1-10000-1-1-1-1-2-211-2-2220000000000-112-2-1-111110000-22110000000000-1-1001-1
χ2922222-2-2222-22-2-222-2-22-12-1-1-1220000-1-1-1-111-2-200000022-2-20000-221-111-1-1112-200000000000011-1-100-1100
χ3022222-2-2222-22-2-222-2-22-12-1-1-1220000-1-1-1-111-2-2000000-2-2220000-221-111-1-111-22000000000000-1-111001-100
χ3122222-2-2222-22-2-222-2-2-12-1222-1-10000-1-1-1-1-2-21122-2-200000000001-1-2211-1-1110000-22-1-1000000000011001-1
χ3222222-2-2222-22-2-222-2-2-12-1222-1-10000-1-1-1-1-2-211-2-22200000000001-1-2211-1-11100002-2110000000000-1-100-11
χ3322-2-222-22-2-20000002-222-22-2-22-22i2i−2i−2i2-2-222-22-200002i−2i00002i2i−2i−2i000000002-2000000002i−2i00000000000000
χ3422-2-222-22-2-20000002-222-22-2-22-2−2i−2i2i2i2-2-222-22-20000−2i2i0000−2i−2i2i2i000000002-200000000−2i2i00000000000000
χ3522-2-22-222-2-2000000-2222-22-2-22-22i2i−2i−2i2-2-22-22-220000−2i2i00002i2i−2i−2i00000000-2200000000−2i2i00000000000000
χ3622-2-22-222-2-2000000-2222-22-2-22-2−2i−2i2i2i2-2-22-22-2200002i−2i0000−2i−2i2i2i00000000-22000000002i−2i00000000000000
χ372-22-2200-22-200000000222-22-2-2-22i−2i2i−2i22-2-20000002i−2i002-2002i−2i2i−2i000000000000000000000000002-22i−2i0000
χ382-22-2200-22-200000000222-22-2-2-22i−2i2i−2i22-2-2000000−2i2i00-22002i−2i2i−2i00000000000000000000000000-22−2i2i0000
χ392-22-2200-22-200000000222-22-2-2-2−2i2i−2i2i22-2-20000002i−2i00-2200−2i2i−2i2i00000000000000000000000000-222i−2i0000
χ402-22-2200-22-200000000222-22-2-2-2−2i2i−2i2i22-2-2000000−2i2i002-200−2i2i−2i2i000000000000000000000000002-2−2i2i0000
χ412-2-22200-2-220000000022-2-2-22-222-2-222-22-200002-20000002-22-2-2200000000000000002-20000002-200000000
χ422-2-22200-2-220000000022-2-2-22-222-2-222-22-20000-22000000-222-2-220000000000000000-22000000-2200000000
χ432-2-22200-2-220000000022-2-2-22-22-222-22-22-200002-2000000-22-222-200000000000000002-2000000-2200000000
χ442-2-22200-2-220000000022-2-2-22-22-222-22-22-20000-220000002-2-222-20000000000000000-220000002-200000000
χ45444444444444444444-2-2-2-2-2-2-2-200001111-2-2-2-200000000000000-2-2-2-2111111000000000000000000000000
χ464444444444-4-4-4-4-4-444-2-2-2-2-2-2-2-200001111-2-2-2-2000000000000002222-1-1-1-111000000000000000000000000
χ4744444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-200001111222200000000000000-22-2211-1-1-1-1000000000000000000000000
χ4844444-4-4444-44-4-444-4-4-2-2-2-2-2-2-2-2000011112222000000000000002-22-2-1-111-1-1000000000000000000000000
χ4944-4-444-44-4-40000004-44-2-4-2224-40000-222-2-224-40000000000000000000000-22000000000000000000000000
χ5044-4-444-44-4-40000004-4-2424-4-4-220000-222-24-4-220000000000000000000000-22000000000000000000000000
χ5144-4-444-44-4-40000004-4-2-22-222-2200001-1-11-22-220000000000000000003-33-31-1000000000000000000000000
χ5244-4-444-44-4-40000004-4-2-22-222-2200001-1-11-22-22000000000000000000-33-331-1000000000000000000000000
χ5344-4-44-444-4-4000000-444-2-4-2224-40000-222-22-2-4400000000000000000000002-2000000000000000000000000
χ5444-4-44-444-4-4000000-44-2424-4-4-220000-222-2-442-200000000000000000000002-2000000000000000000000000
χ5544-4-44-444-4-4000000-44-2-22-222-2200001-1-112-22-20000000000000000003-3-33-11000000000000000000000000
χ5644-4-44-444-4-4000000-44-2-22-222-2200001-1-112-22-2000000000000000000-333-3-11000000000000000000000000
χ574-44-4400-44-4000000004-242-22-4-40000-2-22200000000004-400000000000000000000000000000000-22000000
χ584-44-4400-44-4000000004-242-22-4-40000-2-2220000000000-44000000000000000000000000000000002-2000000
χ594-44-4400-44-400000000-24-2-44-4220000-2-2220000004i−4i00000000000000000000000000000000000000−2i2i0000
χ604-44-4400-44-400000000-24-2-44-4220000-2-222000000−4i4i000000000000000000000000000000000000002i−2i0000
χ614-4-44400-4-44000000004-2-422-2-440000-22-220000000000004-40000000000000000000000000000-2200000000
χ624-4-44400-4-44000000004-2-422-2-440000-22-22000000000000-4400000000000000000000000000002-200000000
χ634-4-44400-4-4400000000-242-4-442-20000-22-2200004-40000000000000000000000000000-220000000000000000
χ644-4-44400-4-4400000000-242-4-442-20000-22-220000-4400000000000000000000000000002-20000000000000000
χ656666-366-3-3-366-3-3-3-3-3-3000000002222000000000000220000-1-1-1-1000000000000220000-1-1-1-1-1-10000000000
χ666666-366-3-3-366-3-3-3-3-3-300000000-2-2-2-2000000000000-2-200001111000000000000-2-200001111110000000000
χ676666-366-3-3-3-6-63333-3-3000000002222000000000000220000-1-1-1-1000000000000-2-20000-1-111110000000000
χ686666-366-3-3-3-6-63333-3-300000000-2-2-2-2000000000000-2-20000111100000000000022000011-1-1-1-10000000000
χ696666-3-6-6-3-3-36-6-3-33333000000002222000000000000-2-20000-1-1-1-10000000000002-2000011-1-1110000000000
χ706666-3-6-6-3-3-36-6-3-3333300000000-2-2-2-20000000000002200001111000000000000-220000-1-111-1-10000000000
χ716666-3-6-6-3-3-3-6633-3-333000000002222000000000000-2-20000-1-1-1-1000000000000-2200001111-1-10000000000
χ726666-3-6-6-3-3-3-6633-3-33300000000-2-2-2-200000000000022000011110000000000002-20000-1-1-1-1110000000000
χ7366-6-6-36-6-33300−3i33i3−3i33i3-33000000002i2i−2i−2i0000000000002i−2i0000−i−iii000000000000000000−ii3−33−30000000000
χ7466-6-6-36-6-33300−3i33i3−3i33i3-3300000000−2i−2i2i2i000000000000−2i2i0000ii−i−i000000000000000000i−i−33−330000000000
χ7566-6-6-36-6-333003i3−3i33i3−3i3-33000000002i2i−2i−2i0000000000002i−2i0000−i−iii000000000000000000−ii−33−330000000000
χ7666-6-6-36-6-333003i3−3i33i3−3i3-3300000000−2i−2i2i2i000000000000−2i2i0000ii−i−i000000000000000000i−i3−33−30000000000
χ7766-6-6-3-66-33300−3i33i33i3−3i33-3000000002i2i−2i−2i000000000000−2i2i0000−i−iii000000000000000000i−i3−3−330000000000
χ7866-6-6-3-66-33300−3i33i33i3−3i33-300000000−2i−2i2i2i0000000000002i−2i0000ii−i−i000000000000000000−ii−333−30000000000
χ7966-6-6-3-66-333003i3−3i3−3i33i33-3000000002i2i−2i−2i000000000000−2i2i0000−i−iii000000000000000000i−i−333−30000000000
χ8066-6-6-3-66-333003i3−3i3−3i33i33-300000000−2i−2i2i2i0000000000002i−2i0000ii−i−i000000000000000000−ii3−3−330000000000
χ818-88-8800-88-800000000-4-4-44-4444000022-2-20000000000000000000000000000000000000000000000000000
χ828-8-88800-8-8800000000-4-4444-44-400002-22-20000000000000000000000000000000000000000000000000000
χ8312-1212-12-6006-6600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ8412-1212-12-6006-660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000
χ8512-12-1212-60066-600000000000000004-4-44000000000000000000-222-20000000000000000000000000000000000
χ8612-12-1212-60066-60000000000000000-444-40000000000000000002-2-220000000000000000000000000000000000

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