Finite Group Databasebeta

← Group #13151351

Character table — Group #13151351

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1222344666226666121233666666444436661212121222444444441212121266666666121222444466121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ61111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-111
χ81111111111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1
χ911111-1-11111-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-111111-11-111-1-1-1-11-11-11-1-1-111-1-111-1-111-1-11-11-1
χ1011111-1-11111-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111111-11-111-1-1-1-1-111-1-11-1-111-1-1-1-111-1-111-11-11
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11-11-111-1-1-1-11-1-11-1111-1-11111-1-1-1-1111-1-11
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11-11-111-1-1-1-1-11-111-111-1-111-1-11111-1-1-111-1
χ1311111-1-1111-11-1-111-1-11111111111111111-1-1-1-1-1-111-1-111-1-11111-11-11-1-111-1-1-11-11-11-1-1-1-11111-1-111-1-1-11-11
χ1411111-1-1111-11-1-111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1111111-11-11-1-111-1-11-1-111-1-1-1-1-111-1-111-1-1111-11-1
χ1511111-1-1111-11-1-111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-11-11-1-111-1-1-111-11-11111-1-111-1-1-1-111-111-1
χ1611111-1-1111-11-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-11-11-1-111-1-11-11-1-111111-1-1-1-11111-1-11-1-11
χ172222222222222222222-1-122-1-120000-1-1-1-1-1-1220022220000000022-1-1-1-1-1-1-1-1220000000000-1-1-1-10000-1-100
χ182222222222222222222-1-122-1-120000-1-1-1-1-1-12200-2-2-2-20000000022-1-1-1-1-1-1-1-1-2-20000000000111100001100
χ19222222222222222222-122-1-122-10000-1-1-1-122-1-100000022220000-1-122-1-1-1-1-1-10000220000000000-1-1-1-100-1-1
χ20222222222222222222-122-1-122-10000-1-1-1-122-1-1000000-2-2-2-20000-1-122-1-1-1-1-1-10000-2-2000000000011110011
χ212222222222-2-2-2-2-2-2222-1-122-1-120000-1-1-1-1-1-12200222200000000-2-2111111-1-1-2-20000000000-1-1-1-100001100
χ222222222222-2-2-2-2-2-2222-1-122-1-120000-1-1-1-1-1-12200-2-2-2-200000000-2-2111111-1-122000000000011110000-1-100
χ232222222222-2-2-2-2-2-222-122-1-122-10000-1-1-1-122-1-10000002222000011-2-21111-1-10000-2-20000000000-1-1-1-10011
χ242222222222-2-2-2-2-2-222-122-1-122-10000-1-1-1-122-1-1000000-2-2-2-2000011-2-21111-1-10000220000000000111100-1-1
χ2522222-2-22222-222-2-2-2-22-1-122-1-120000-1-1-1-111-2-20022-2-2000000002-2-11-1-111112-20000000000-1-1110000-1100
χ2622222-2-22222-222-2-2-2-22-1-122-1-120000-1-1-1-111-2-200-2-222000000002-2-11-1-11111-22000000000011-1-100001-100
χ2722222-2-22222-222-2-2-2-2-122-1-122-10000-1-1-1-1-2-21100000022-2-20000-112-2-1-1111100002-20000000000-1-11100-11
χ2822222-2-22222-222-2-2-2-2-122-1-122-10000-1-1-1-1-2-211000000-2-2220000-112-2-1-111110000-22000000000011-1-1001-1
χ2922222-2-2222-22-2-222-2-22-1-122-1-120000-1-1-1-111-2-20022-2-200000000-221-111-1-111-220000000000-1-11100001-100
χ3022222-2-2222-22-2-222-2-22-1-122-1-120000-1-1-1-111-2-200-2-22200000000-221-111-1-1112-2000000000011-1-10000-1100
χ3122222-2-2222-22-2-222-2-2-122-1-122-10000-1-1-1-1-2-21100000022-2-200001-1-2211-1-1110000-220000000000-1-111001-1
χ3222222-2-2222-22-2-222-2-2-122-1-122-10000-1-1-1-1-2-211000000-2-22200001-1-2211-1-11100002-2000000000011-1-100-11
χ3322-2-22002-2-20000000022-22-22-2-22i2i−2i−2i22-2-2000000002-2002i−2i2i2i−2i−2i0000000000000000000000002-2002i−2i0000
χ3422-2-22002-2-20000000022-22-22-2-22i2i−2i−2i22-2-200000000-2200−2i2i2i2i−2i−2i000000000000000000000000-2200−2i2i0000
χ3522-2-22002-2-20000000022-22-22-2-2−2i−2i2i2i22-2-2000000002-200−2i2i−2i−2i2i2i0000000000000000000000002-200−2i2i0000
χ3622-2-22002-2-20000000022-22-22-2-2−2i−2i2i2i22-2-200000000-22002i−2i−2i−2i2i2i000000000000000000000000-22002i−2i0000
χ372-22-2200-22-20000000022-2-22-22-22i−2i2i−2i2-22-20000002-2002i−2i002i−2i2i−2i00000000000000000000002-2002i−2i000000
χ382-22-2200-22-20000000022-2-22-22-22i−2i2i−2i2-22-2000000-2200−2i2i002i−2i2i−2i0000000000000000000000-2200−2i2i000000
χ392-22-2200-22-20000000022-2-22-22-2−2i2i−2i2i2-22-20000002-200−2i2i00−2i2i−2i2i00000000000000000000002-200−2i2i000000
χ402-22-2200-22-20000000022-2-22-22-2−2i2i−2i2i2-22-2000000-22002i−2i00−2i2i−2i2i0000000000000000000000-22002i−2i000000
χ412-2-2222-2-2-220000002-2222-2-2-2-222-2-222-2-222-22-22-2000000002-2-22000000002-20000002-20000000000000000
χ422-2-2222-2-2-220000002-2222-2-2-2-22-222-22-2-222-22-2-2200000000-222-2000000002-2000000-220000000000000000
χ432-2-222-22-2-22000000-22222-2-2-2-222-2-222-2-22-22-22-22000000002-2-2200000000-22000000-220000000000000000
χ442-2-222-22-2-22000000-22222-2-2-2-22-222-22-2-22-22-222-200000000-222-200000000-220000002-20000000000000000
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
χ4944-4-44004-4-4000000004-224-4-22-40000-2-222000000004-400000000000000000000000000000000-2200000000
χ5044-4-44004-4-4000000004-224-4-22-40000-2-22200000000-44000000000000000000000000000000002-200000000
χ5144-4-44004-4-400000000-24-4-224-420000-2-2220000000000004i−4i00000000000000000000000000000000−2i2i0000
χ5244-4-44004-4-400000000-24-4-224-420000-2-222000000000000−4i4i000000000000000000000000000000002i−2i0000
χ534-44-4400-44-4000000004-22-442-2-40000-22-220000004-400000000000000000000000000000000-220000000000
χ544-44-4400-44-4000000004-22-442-2-40000-22-22000000-44000000000000000000000000000000002-20000000000
χ554-44-4400-44-400000000-24-42-2-4420000-22-2200000000004i−4i00000000000000000000000000000000−2i2i000000
χ564-44-4400-44-400000000-24-42-2-4420000-22-220000000000−4i4i000000000000000000000000000000002i−2i000000
χ574-4-4444-4-4-440000004-44-2-2-4-42240000-222-2-224-40000000000000000000000-22000000000000000000000000
χ584-4-4444-4-4-440000004-4-24422-4-4-20000-222-24-4-220000000000000000000000-22000000000000000000000000
χ594-4-4444-4-4-440000004-4-2-2-22222-200001-1-11-22-220000000000000000003-33-31-1000000000000000000000000
χ604-4-4444-4-4-440000004-4-2-2-22222-200001-1-11-22-22000000000000000000-33-331-1000000000000000000000000
χ614-4-444-44-4-44000000-444-2-2-4-42240000-222-22-2-4400000000000000000000002-2000000000000000000000000
χ624-4-444-44-4-44000000-44-24422-4-4-20000-222-2-442-200000000000000000000002-2000000000000000000000000
χ634-4-444-44-4-44000000-44-2-2-22222-200001-1-112-22-20000000000000000003-3-33-11000000000000000000000000
χ644-4-444-44-4-44000000-44-2-2-22222-200001-1-112-22-2000000000000000000-333-3-11000000000000000000000000
χ656666-366-3-3-366-3-3-3-3-3-3000000002222000000002200000000-1-1-1-10000000000002200-1-1-1-1-1-1000000000000
χ666666-366-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-2000000001111000000000000-2-200111111000000000000
χ676666-366-3-3-3-6-63333-3-3000000002222000000002200000000-1-1-1-1000000000000-2-200-1-11111000000000000
χ686666-366-3-3-3-6-63333-3-300000000-2-2-2-200000000-2-2000000001111000000000000220011-1-1-1-1000000000000
χ696666-3-6-6-3-3-36-6-3-3333300000000222200000000-2-200000000-1-1-1-10000000000002-20011-1-111000000000000
χ706666-3-6-6-3-3-36-6-3-3333300000000-2-2-2-20000000022000000001111000000000000-2200-1-111-1-1000000000000
χ716666-3-6-6-3-3-3-6633-3-33300000000222200000000-2-200000000-1-1-1-1000000000000-22001111-1-1000000000000
χ726666-3-6-6-3-3-3-6633-3-33300000000-2-2-2-200000000220000000011110000000000002-200-1-1-1-111000000000000
χ736-6-66-36-633-300−3i33i3−3i33i3-33000000002-2-22000000002-200000000-111-10000000000000000-11−i3i3−i3i3000000000000
χ746-6-66-36-633-300−3i33i3−3i33i3-3300000000-222-200000000-22000000001-1-1100000000000000001-1i3−i3i3−i3000000000000
χ756-6-66-36-633-3003i3−3i33i3−3i3-33000000002-2-22000000002-200000000-111-10000000000000000-11i3−i3i3−i3000000000000
χ766-6-66-36-633-3003i3−3i33i3−3i3-3300000000-222-200000000-22000000001-1-1100000000000000001-1−i3i3−i3i3000000000000
χ776-6-66-3-6633-300−3i33i33i3−3i33-3000000002-2-2200000000-2200000000-111-100000000000000001-1−i3i3i3−i3000000000000
χ786-6-66-3-6633-300−3i33i33i3−3i33-300000000-222-2000000002-2000000001-1-110000000000000000-11i3−i3−i3i3000000000000
χ796-6-66-3-6633-3003i3−3i3−3i33i33-3000000002-2-2200000000-2200000000-111-100000000000000001-1i3−i3−i3i3000000000000
χ806-6-66-3-6633-3003i3−3i3−3i33i33-300000000-222-2000000002-2000000001-1-110000000000000000-11−i3i3i3−i3000000000000
χ8188-8-88008-8-800000000-4-44-44-444000022-2-20000000000000000000000000000000000000000000000000000
χ828-88-8800-88-800000000-4-444-44-4400002-22-20000000000000000000000000000000000000000000000000000
χ831212-12-12-600-66600000000000000004i4i−4i−4i000000000000000000−2i−2i2i2i0000000000000000000000000000000000
χ841212-12-12-600-6660000000000000000−4i−4i4i4i0000000000000000002i2i−2i−2i0000000000000000000000000000000000
χ8512-1212-12-6006-6600000000000000004i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ8612-1212-12-6006-660000000000000000−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000

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