Finite Group Databasebeta

← Group #13140921

Character table — Group #13140921

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order122234466612123366666641212366612121212224488888888121212121212121212126612122424242424242424444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111
χ511111111111111111111-1-1-111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1111-1-111
χ711111111111111111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1-1
χ92222222222222-122-1-1-12222-1-1-1-1-1-122222200000000-1-122-1-1-1-1-1-1-1-1-1-10000000002000-1-100
χ102222222222222-122-1-1-12222-1-1-1-1-1-122-2-2-2-200000000-1-122-1-1-1-1-1-11111000000000-20001100
χ112222222222222-122-1-1-12-2-2-2-1-1-1-1-1-12222220000000011-2-2-1-11111-1-1-1-1000000000-20001100
χ122222222222222-122-1-1-12-2-2-2-1-1-1-1-1-122-2-2-2-20000000011-2-2-1-1111111110000000002000-1-100
χ13222222222222-12-1-1222-1222-1-1-1-122-1-100000000222222-1-1-1-1-1-1-1-100000000-1-1-1-12000000-1-1
χ14222222222222-12-1-1222-1222-1-1-1-122-1-100000000-2-2-2-222-1-1-1-1-1-1-1-1000000001111-200000011
χ15222222222222-12-1-1222-1-2-2-2-1-1-1-122-1-1000000002222-2-211-1-1111100000000-1-1-1-1-200000011
χ16222222222222-12-1-1222-1-2-2-2-1-1-1-122-1-100000000-2-2-2-2-2-211-1-111110000000011112000000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-222-2-2000000000000-2-2000022-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-222000000000000-2-20000-2-22200000000000000000
χ1922222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-222-2-200000000−i3i30011−i3−i3i3i3-1-1110000000000000−i3i300
χ2022222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-222-2-200000000i3−i30011i3i3−i3−i3-1-1110000000000000i3−i300
χ2122222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-2-2-22200000000−i3i30011−i3−i3i3i311-1-10000000000000i3−i300
χ2222222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-2-2-22200000000i3−i30011i3i3−i3−i311-1-10000000000000−i3i300
χ2322-2-22002-2-200222-22-2-2-200022-2-200002-20022−2−222−2−200000000002-20022−2−222−2−2000000000
χ2422-2-22002-2-200222-22-2-2-200022-2-200002-200−2−222−2−22200000000002-200−2−222−2−222000000000
χ2522-2-22002-2-200222-22-2-2-200022-2-20000-220022−2−2−2−2220000000000-220022−2−2−2−222000000000
χ2622-2-22002-2-200222-22-2-2-200022-2-20000-2200−2−22222−2−20000000000-2200−2−22222−2−2000000000
χ272-22-222-2-22-22-222-2-2-22-220002-2-222-22-200002i−2i2i−2i000000002-2000000002i−2i2i−2i0000000000000
χ282-22-222-2-22-22-222-2-2-22-220002-2-222-22-20000−2i2i−2i2i000000002-200000000−2i2i−2i2i0000000000000
χ292-22-22-22-22-2-2222-2-2-22-220002-2-22-22-22000000002-22-20000-220000000000002-22-2000000000
χ302-22-22-22-22-2-2222-2-2-22-220002-2-22-22-2200000000-22-220000-22000000000000-22-22000000000
χ312-22-22-22-22-2-22-1211-22-2-1000-111-1-221-1000000002-22-200−i3i31-1−i3i3−i3i300000000-11-110000000−i3i3
χ322-22-22-22-22-2-22-1211-22-2-1000-111-1-221-1000000002-22-200i3−i31-1i3−i3i3−i300000000-11-110000000i3−i3
χ332-22-22-22-22-2-22-1211-22-2-1000-111-1-221-100000000-22-2200−i3i31-1−i3i3−i3i3000000001-11-10000000i3−i3
χ342-22-22-22-22-2-22-1211-22-2-1000-111-1-221-100000000-22-2200i3−i31-1i3−i3i3−i3000000001-11-10000000−i3i3
χ352-2-22200-2-220022-22-2-22-20002-22-20000002i−2i−i2i2i2−i22−2−220000000000002i−2i−i2i2i2−i22−2−22000000000
χ362-2-22200-2-220022-22-2-22-20002-22-20000002i−2ii2−i2−i2i2−222−20000000000002i−2ii2−i2−i2i2−222−2000000000
χ372-2-22200-2-220022-22-2-22-20002-22-2000000−2i2i−i2i2i2−i2−222−2000000000000−2i2i−i2i2i2−i2−222−2000000000
χ382-2-22200-2-220022-22-2-22-20002-22-2000000−2i2ii2−i2−i2i22−2−22000000000000−2i2ii2−i2−i2i22−2−22000000000
χ39444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2000000000000-2-2-2-2111111000000000000000000000
χ40444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2000000000000222211-1-1-1-1000000000000000000000
χ4144444-4-4444-4-4-24-2-2444-2000-2-2-2-2-4-4220000000000000000220000000000000000000000000
χ4244444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000000000−2i32i300-1-1i3i3−i3−i3000000000000000000000
χ4344444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000000000002i3−2i300-1-1−i3−i3i3i3000000000000000000000
χ4444-4-44004-4-4004-24-4-222-4000-2-22200004-400000000000000000000-220000000000000000000
χ4544-4-44004-4-4004-24-4-222-4000-2-2220000-44000000000000000000002-20000000000000000000
χ4644-4-44004-4-400-24-224-4-42000-2-2220000000000002222−22−22000000000000000000−2−222000000000
χ4744-4-44004-4-400-24-224-4-42000-2-222000000000000−22−22222200000000000000000022−2−2000000000
χ484-44-444-4-44-44-44-2-4-42-224000-222-2-224-40000000000000000-220000000000000000000000000
χ494-44-444-4-44-44-4-2422-44-4-2000-222-24-4-220000000000000000-220000000000000000000000000
χ504-44-444-4-44-44-4-2-2222-22-20001-1-11-22-2200000000000000001-13-3-33000000000000000000000
χ514-44-444-4-44-44-4-2-2222-22-20001-1-11-22-2200000000000000001-1-333-3000000000000000000000
χ524-44-44-44-44-4-444-2-4-42-224000-222-22-2-4400000000000000002-20000000000000000000000000
χ534-44-44-44-44-4-44-2-2222-22-20001-1-112-22-200000000000000−2i32i3-11i3−i3i3−i3000000000000000000000
χ544-44-44-44-44-4-44-2-2222-22-20001-1-112-22-2000000000000002i3−2i3-11−i3i3−i3i3000000000000000000000
χ554-4-44400-4-44004-2-4422-2-4000-22-220000004i−4i00000000000000000000−2i2i00000000000000000
χ564-4-44400-4-44004-2-4422-2-4000-22-22000000−4i4i000000000000000000002i−2i00000000000000000
χ574-4-44400-4-4400-242-2-4-442000-22-2200000000000022−22−2222000000000000000000−222−2000000000
χ584-4-44400-4-4400-242-2-4-442000-22-22000000000000−222222−220000000000000000002−2−22000000000
χ596666-366-3-3-3-3-3000000006-3-30000000000002222000000000000000000-1-1-1-10000002-1-10000
χ606666-366-3-3-3-3-3000000006-3-3000000000000-2-2-2-20000000000000000001111000000-2110000
χ616666-366-3-3-3-3-300000000-6330000000000002222000000000000000000-1-1-1-1000000-2110000
χ626666-366-3-3-3-3-300000000-633000000000000-2-2-2-200000000000000000011110000002-1-10000
χ636-66-6-36-63-33-33000000000−3i33i30000000000002i−2i2i−2i000000000000000000−ii−ii00000003−30000
χ646-66-6-36-63-33-33000000000−3i33i3000000000000−2i2i−2i2i000000000000000000i−ii−i0000000−330000
χ656-66-6-36-63-33-330000000003i3−3i30000000000002i−2i2i−2i000000000000000000−ii−ii0000000−330000
χ666-66-6-36-63-33-330000000003i3−3i3000000000000−2i2i−2i2i000000000000000000i−ii−i00000003−30000
χ6788-8-88008-8-800-4-4-44-444400022-2-200000000000000000000000000000000000000000000000
χ688-8-88800-8-8800-4-44-444-440002-22-200000000000000000000000000000000000000000000000
χ6912121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000000
χ701212-12-12-600-66600000000000000000000000002222−22−22000000000000000000−2−2220000000000000
χ711212-12-12-600-6660000000000000000000000000−22−22222200000000000000000022−2−20000000000000
χ7212-1212-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-60066-60000000000000000000000000−2i22i22i2−2i2000000000000000000i2−i2−i2i20000000000000
χ7412-12-1212-60066-600000000000000000000000002i2−2i2−2i22i2000000000000000000−i2i2i2−i20000000000000

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