Finite Group Databasebeta

← Group #13140617

Character table — Group #13140617

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order1222344666121233666666266366612121212446666666612124444488881212121224242424242424244121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111-1-11111111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ511111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-111
χ92222222222222-122-1-1-12222-1-1-1-1-12-120022-1-1-1-1-1-1-1-10220022000000-1-1-1-10000000-1-100
χ102222222222222-122-1-1-12222-1-1-1-1-12-120022-1-1-1-1-1-1-1-10-2-200-2-2000000111100000001100
χ112222222222222-122-1-1-12-2-2-2-1-1-1-1-12-1200-2-2111111-1-102200-2-200000011110000000-1-100
χ122222222222222-122-1-1-12-2-2-2-1-1-1-1-12-1200-2-2111111-1-10-2-20022000000-1-1-1-100000001100
χ13222222222222-12-1-1222-1222-1-1-1-12-12-100-1-122-1-1-1-1-1-100022002200000000-1-1-1-100000-1-1
χ14222222222222-12-1-1222-1222-1-1-1-12-12-100-1-122-1-1-1-1-1-1000-2-200-2-20000000011110000011
χ15222222222222-12-1-1222-1-2-2-2-1-1-1-12-12-10011-2-21111-1-10002200-2-200000000111100000-1-1
χ16222222222222-12-1-1222-1-2-2-2-1-1-1-12-12-10011-2-21111-1-1000-2-2002200000000-1-1-1-10000011
χ1722222-2-2222-2-2222222220002222-2-2-2-22200000000-2-2-20000000022-2-2000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-200000000-2-2200000000-2-222000000000000000
χ192-22-22002-2-200222-2-2-22-200022-2-200002i−2i0000000000000002−2−i2i22i−2i0022−2−2−i2−i2i2i20000000
χ202-22-22002-2-200222-2-2-22-200022-2-200002i−2i000000000000000−22i2−i22i−2i00−2−222i2i2−i2−i20000000
χ212-22-22002-2-200222-2-2-22-200022-2-20000−2i2i0000000000000002−2i2−i2−2i2i0022−2−2i2i2−i2−i20000000
χ222-22-22002-2-200222-2-2-22-200022-2-20000−2i2i000000000000000−22−i2i2−2i2i00−2−222−i2−i2i2i20000000
χ232-2-2222-2-2-222-222-2-2-22-220002-2-2222-2-200000000002-202i−2i0000000000000000000002i−2i00
χ242-2-2222-2-2-222-222-2-2-22-220002-2-2222-2-200000000002-20−2i2i000000000000000000000−2i2i00
χ252-2-2222-2-2-222-22-1-2-21-112000-111-1-121-20000−i3i3−i3−i3i3i3-1102i−2i00000000003−33−30000000−ii00
χ262-2-2222-2-2-222-22-1-2-21-112000-111-1-121-20000−i3i3−i3−i3i3i3-110−2i2i0000000000−33−330000000i−i00
χ272-2-2222-2-2-222-22-1-2-21-112000-111-1-121-20000i3−i3i3i3−i3−i3-1102i−2i0000000000−33−330000000−ii00
χ282-2-2222-2-2-222-22-1-2-21-112000-111-1-121-20000i3−i3i3i3−i3−i3-110−2i2i00000000003−33−30000000i−i00
χ292-2-222-22-2-22-2222-2-2-22-220002-2-22-2-2220000000000-220002-20000000000000000000002-2
χ302-2-222-22-2-22-2222-2-2-22-220002-2-22-2-2220000000000-22000-22000000000000000000000-22
χ312-2-222-22-2-22-22-1211-22-2-1000-111-1-212-100−i3i300−i3i3−i3i31-10002-2000000000000−i3i3−i3i300000-11
χ322-2-222-22-2-22-22-1211-22-2-1000-111-1-212-100−i3i300−i3i3−i3i31-1000-22000000000000i3−i3i3−i3000001-1
χ332-2-222-22-2-22-22-1211-22-2-1000-111-1-212-100i3−i300i3−i3i3−i31-10002-2000000000000i3−i3i3−i300000-11
χ342-2-222-22-2-22-22-1211-22-2-1000-111-1-212-100i3−i300i3−i3i3−i31-1000-22000000000000−i3i3−i3i3000001-1
χ35444444444444-2-2-2-2-2-2-2-24441111-2-2-2-200-2-2-2-21111110000000000000000000000000000
χ36444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2002222-1-1-1-1110000000000000000000000000000
χ3744444-4-4444-4-44-244-2-2-24000-2-2-2-22-42-40000000000220000000000000000000000000000
χ3844444-4-4444-4-4-24-2-2444-2000-2-2-2-2-42-420000000000220000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000003-3-33-1-10000000000000000000000000000
χ4044444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000-333-3-1-10000000000000000000000000000
χ4144-4-4400-44-40044-444-4-4-40004-44-400000000000000000000000000000000000000000000
χ4244-4-4400-44-4004-2-44-222-4000-22-22000000000000000000000000000006−6−6600000000000
χ4344-4-4400-44-4004-2-44-222-4000-22-2200000000000000000000000000000−666−600000000000
χ4444-4-4400-44-400-242-24-4-42000-22-220000000000000000000000000000000006−6−660000000
χ4544-4-4400-44-400-242-24-4-42000-22-22000000000000000000000000000000000−666−60000000
χ464-44-44004-4-4004-24-422-2-4000-2-22200000000000000000000022−22000000−2−22200000000000
χ474-44-44004-4-4004-24-422-2-4000-2-222000000000000000000000−222200000022−2−200000000000
χ484-44-44004-4-400-24-22-4-442000-2-22200000000000000000000000−2i22i200000000i2i2−i2−i20000000
χ494-44-44004-4-400-24-22-4-442000-2-222000000000000000000000002i2−2i200000000−i2−i2i2i20000000
χ504-4-4444-4-4-444-4-2422-44-4-2000-222-24-2-420000000000-220000000000000000000000000000
χ514-4-4444-4-4-444-4-2-2222-22-20001-1-11-2-2220000−2i32i3i3i3−i3−i31-10000000000000000000000000000
χ524-4-4444-4-4-444-4-2-2222-22-20001-1-11-2-22200002i3−2i3−i3−i3i3i31-10000000000000000000000000000
χ534-4-444-44-4-44-444-2-4-42-224000-222-22-4-2400000000002-20000000000000000000000000000
χ544-4-444-44-4-44-44-2-2222-22-20001-1-1122-2-200−2i32i300i3−i3i3−i3-110000000000000000000000000000
χ554-4-444-44-4-44-44-2-2222-22-20001-1-1122-2-2002i3−2i300−i3i3−i3i3-110000000000000000000000000000
χ566666-366-3-3-3-3-3000000006-3-300000000220000000000200000000-1-1-1-1000000002-1-10000
χ576666-366-3-3-3-3-3000000006-3-300000000-2-20000000000-200000000111100000000-2110000
χ586666-366-3-3-3-3-300000000-63300000000220000000000200000000-1-1-1-100000000-2110000
χ596666-366-3-3-3-3-300000000-63300000000-2-20000000000-2000000001111000000002-1-10000
χ606666-3-6-6-3-3-333000000000−3i33i300000000220000000000-200000000-1-111000000000−i3i30000
χ616666-3-6-6-3-3-333000000000−3i33i300000000-2-2000000000020000000011-1-1000000000i3−i30000
χ626666-3-6-6-3-3-3330000000003i3−3i300000000220000000000-200000000-1-111000000000i3−i30000
χ636666-3-6-6-3-3-3330000000003i3−3i300000000-2-2000000000020000000011-1-1000000000−i3i30000
χ6488-8-8800-88-800-4-44-4-44440002-22-200000000000000000000000000000000000000000000
χ658-88-88008-8-800-4-4-4444-4400022-2-200000000000000000000000000000000000000000000
χ661212-12-12-6006-660000000000000000000000000000000000000000000023−23000000000000000
χ671212-12-12-6006-6600000000000000000000000000000000000000000000−2323000000000000000
χ6812-1212-12-600-6660000000000000000000004i−4i0000000000000000000−2i2i00000000000000000
χ6912-1212-12-600-666000000000000000000000−4i4i00000000000000000002i−2i00000000000000000
χ7012-12-1212-612-1266-6-6600000000000000000000000000000000000000000000000000000000000
χ7112-12-1212-6-121266-66-600000000000000000000000000000000000000000000000000000000000

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