Finite Group Databasebeta

← Group #13140536

Character table — Group #13140536

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222224466666666888121212121212121218182424242424242424242436363636363636363636363636363636363636363672727272727272
order1222344666121233666666266366612121212446666666612124444488881212121224242424242424244121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111111111111-1-11111111111-111-1-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ511111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111
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
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-11111
χ92222222222222-122-1-12-1222-1-1-1-12-1-122222-1-1-1-1-1-1-1-1200000000-1-1-1-100000000200-1-100
χ102222222222222-122-1-12-1222-1-1-1-12-1-12-2-222-1-1-1-1-1-1-1-1-200000000111100000000-2001100
χ112222222222222-122-1-12-1-2-2-2-1-1-1-12-1-1222-2-2111111-1-1200000000-1-1-1-100000000-2001100
χ122222222222222-122-1-12-1-2-2-2-1-1-1-12-1-12-2-2-2-2111111-1-1-200000000111100000000200-1-100
χ13222222222222-12-1-122-12222-1-1-1-1-122-100-1-122-1-1-1-1-1-100022002200000000-1-1-1-100000-1-1
χ14222222222222-12-1-122-12222-1-1-1-1-122-100-1-122-1-1-1-1-1-1000-2-200-2-20000000011110000011
χ15222222222222-12-1-122-12-2-2-2-1-1-1-1-122-10011-2-21111-1-10002200-2-200000000111100000-1-1
χ16222222222222-12-1-122-12-2-2-2-1-1-1-1-122-10011-2-21111-1-1000-2-2002200000000-1-1-1-10000011
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
χ1922222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-22200−i3i3−i3−i3i3i311-200000000-1-11100000000000−i3i300
χ2022222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-22200i3−i3i3i3−i3−i311-200000000-1-11100000000000i3−i300
χ2122222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-2-2-200−i3i3−i3−i3i3i31120000000011-1-100000000000i3−i300
χ2222222-2-2222-2-22-122-1-12-1000-1-1-1-1-211-2-2-200i3−i3i3i3−i3−i31120000000011-1-100000000000−i3i300
χ232-22-2200-2-2200222-22-2-2-200022-2-200002i−2i0000000000000002−2−i2i22i−2i0022−2−2−i2−i2i2i20000000
χ242-22-2200-2-2200222-22-2-2-200022-2-200002i−2i000000000000000−22i2−i22i−2i00−2−222i2i2−i2−i20000000
χ252-22-2200-2-2200222-22-2-2-200022-2-20000−2i2i0000000000000002−2i2−i2−2i2i0022−2−2i2i2−i2−i20000000
χ262-22-2200-2-2200222-22-2-2-200022-2-20000−2i2i000000000000000−22−i2i2−2i2i00−2−222−i2−i2i2i20000000
χ272-2-2222-2-22-22-222-2-2-2-2220002-2-2222-2-200000000002-202i−2i00000000000000000002i−2i0000
χ282-2-2222-2-22-22-222-2-2-2-2220002-2-2222-2-200000000002-20−2i2i0000000000000000000−2i2i0000
χ292-2-222-22-22-2-2222-2-2-2-2220002-2-22-2-2220000000000-220002-20000000000000000000002-2
χ302-2-222-22-22-2-2222-2-2-2-2220002-2-22-2-2220000000000-22000-22000000000000000000000-22
χ312-2-222-22-22-2-22-1211-2-2-12000-111-11-22-100−i3i300−i3i3−i3i31-10002-2000000000000−i3i3−i3i300000-11
χ322-2-222-22-22-2-22-1211-2-2-12000-111-11-22-100−i3i300−i3i3−i3i31-1000-22000000000000i3−i3i3−i3000001-1
χ332-2-222-22-22-2-22-1211-2-2-12000-111-11-22-100i3−i300i3−i3i3−i31-10002-2000000000000i3−i3i3−i300000-11
χ342-2-222-22-22-2-22-1211-2-2-12000-111-11-22-100i3−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
χ3744444-4-4444-4-4-24-2-244-24000-2-2-2-22-4-420000000000220000000000000000000000000000
χ3844444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000−2i32i3i3i3−i3−i3-1-10000000000000000000000000000
χ3944444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200002i3−2i3−i3−i3i3i3-1-10000000000000000000000000000
χ4044-4-44004-4-40044-44-44-4-40004-44-400000000000000000000000000000000000000000000
χ4144-4-44004-4-4004-2-442-2-42000-22-2200000000000000000000000000023−23000000000000000
χ4244-4-44004-4-4004-2-442-2-42000-22-22000000000000000000000000000−2323000000000000000
χ4344-4-44004-4-400-242-2-442-4000-22-220000000000000000000000000000000006−6−660000000
χ4444-4-44004-4-400-242-2-442-4000-22-22000000000000000000000000000000000−666−60000000
χ454-44-4400-4-44004-24-4-22-42000-2-22200004i−4i0000000000000000000−2i2i00000000000000000
χ464-44-4400-4-44004-24-4-22-42000-2-2220000−4i4i00000000000000000002i−2i00000000000000000
χ474-44-4400-4-4400-24-224-42-4000-2-22200000000000000000000000−2i22i200000000i2i2−i2−i20000000
χ484-44-4400-4-4400-24-224-42-4000-2-222000000000000000000000002i2−2i200000000−i2−i2i2i20000000
χ494-4-4444-4-44-44-44-2-4-4224-2000-222-24-22-40000000000-220000000000000000000000000000
χ504-4-4444-4-44-44-4-2422-4-4-24000-222-2-24-420000000000-220000000000000000000000000000
χ514-4-4444-4-44-44-4-2-22222-2-20001-1-11-2-2220000003-3-331-10000000000000000000000000000
χ524-4-4444-4-44-44-4-2-22222-2-20001-1-11-2-222000000-333-31-10000000000000000000000000000
χ534-4-444-44-44-4-444-2-4-4224-2000-222-2-42-2400000000002-20000000000000000000000000000
χ544-4-444-44-44-4-44-2-22222-2-20001-1-1122-2-200−2i32i300i3−i3i3−i3-110000000000000000000000000000
χ554-4-444-44-44-4-44-2-22222-2-20001-1-1122-2-2002i3−2i300−i3i3−i3i3-110000000000000000000000000000
χ566666-366-3-3-3-3-3000000006-3-3000000000000000000000220022000000-1-1-1-100000-1-10000
χ576666-366-3-3-3-3-3000000006-3-3000000000000000000000-2-200-2-2000000111100000110000
χ586666-366-3-3-3-3-300000000-6330000000000000000000002200-2-2000000111100000-1-10000
χ596666-366-3-3-3-3-300000000-633000000000000000000000-2-20022000000-1-1-1-100000110000
χ606-6-66-36-63-33-33000000000−3i33i30000000000000000000002i−2i00000000003−33−300000−ii0000
χ616-6-66-36-63-33-33000000000−3i33i3000000000000000000000−2i2i0000000000−33−3300000i−i0000
χ626-6-66-36-63-33-330000000003i3−3i30000000000000000000002i−2i0000000000−33−3300000−ii0000
χ636-6-66-36-63-33-330000000003i3−3i3000000000000000000000−2i2i00000000003−33−300000i−i0000
χ6488-8-88008-8-800-4-44-44-4440002-22-200000000000000000000000000000000000000000000
χ658-88-8800-8-8800-4-4-44-444400022-2-200000000000000000000000000000000000000000000
χ6612121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000
χ671212-12-12-600-66600000000000000000000000000000000000000000000006−6−6600000000000
χ681212-12-12-600-6660000000000000000000000000000000000000000000000−666−600000000000
χ6912-1212-12-60066-60000000000000000000000000000000000000022−22000000−2−22200000000000
χ7012-1212-12-60066-600000000000000000000000000000000000000−222200000022−2−200000000000
χ7112-12-1212-6-12126-666-600000000000000000000000000000000000000000000000000000000000

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