Finite Group Databasebeta

← Group #13165495

Character table — Group #13165495

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222244444444668888888812121212181818181818242424242424242424242424242424242424242427272727363636363636363636365454545472727272
order12223666336666664433666666224444888866666666121212121212121212121212444422441212242424248888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ51111111111111111-1-11111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-11111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1
χ71111111111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ81111111111111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ91-11-11-1-111111-1-1-1-1i−i111-11-1-1-11-1i−i-11ii−i−i1-11-111-1-1i−iii−i−ii−iii−i−iii−i−i1-1i−i1-1ii−i−i11-1-11-1i−i
χ101-11-11-1-111111-1-1-1-1i−i111-11-1-1-11-1−ii-11−i−iii1-11-111-1-1−iiii−i−i−ii−i−iiiii−i−i-11i−i1-1−i−iii-1-111-11i−i
χ111-11-11-1-111111-1-1-1-1i−i111-11-1-1-1-11i−i-11−i−iii-11-11-1-111i−iii−i−ii−iii−i−iii−i−i1-1−ii1-1−i−iii-1-1111-1−ii
χ121-11-11-1-111111-1-1-1-1i−i111-11-1-1-1-11−ii-11ii−i−i-11-11-1-111−iiii−i−i−ii−i−iiiii−i−i-11−ii1-1ii−i−i11-1-1-11−ii
χ131-11-11-1-111111-1-1-1-1−ii111-11-1-1-11-1i−i-11ii−i−i1-11-111-1-1i−i−i−iiii−iii−i−i−i−iii-11−ii1-1ii−i−i-1-111-11−ii
χ141-11-11-1-111111-1-1-1-1−ii111-11-1-1-11-1−ii-11−i−iii1-11-111-1-1−ii−i−iii−ii−i−iii−i−iii1-1−ii1-1−i−iii11-1-11-1−ii
χ151-11-11-1-111111-1-1-1-1−ii111-11-1-1-1-11i−i-11−i−iii-11-11-1-111i−i−i−iiii−iii−i−i−i−iii-11i−i1-1−i−iii11-1-1-11i−i
χ161-11-11-1-111111-1-1-1-1−ii111-11-1-1-1-11−ii-11ii−i−i-11-11-1-111−ii−i−iii−ii−i−iii−i−iii1-1i−i1-1ii−i−i-1-1111-1i−i
χ17222222222222222222222222220000-2-2000000000000002222000000-2-2-2-20000-2-2000000000000
χ182222222222222222-2-2222222220000-2-200000000000000-2-2-2-200000022220000-2-2000000000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-12222222222-1-122-1-1-1-1-1-1000022-1-1-1-100000000-1-1-1-1-1-100000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-122-1-1-1-1110000-2-2111100000000-1-1111100000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-22222-2-2-2-211-2-21111-1-1000022-1-1-1-100000000-1-1111100000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-222222211-2-21111110000-2-2111100000000-1-1-1-1-1-100000000
χ2322-2-222-2-222-2-222-2-20022-22-22-2-2000000i2−i2i2−i2000000000000000000002i−2i2i−2i000000i2−i2i2−i22−22−20000
χ2422-2-222-2-222-2-222-2-20022-22-22-2-2000000i2−i2i2−i200000000000000000000−2i2i−2i2i000000i2−i2i2−i2−22−220000
χ2522-2-222-2-222-2-222-2-20022-22-22-2-2000000−i2i2−i2i2000000000000000000002i−2i2i−2i000000−i2i2−i2i2−22−220000
χ2622-2-222-2-222-2-222-2-20022-22-22-2-2000000−i2i2−i2i200000000000000000000−2i2i−2i2i000000−i2i2−i2i22−22−20000
χ272-22-22-2-222222-2-2-2-22i−2i222-22-2-2-200002-2000000000000002i2i−2i−2i000000−2i−2i2i2i0000-22000000000000
χ282-22-22-2-222222-2-2-2-2−2i2i222-22-2-2-200002-200000000000000−2i−2i2i2i0000002i2i−2i−2i0000-22000000000000
χ292-22-2-111-12222-2-2-2-200-1-1-11-11112-22i−2i-222i2i−2i−2i-112-2-1-111−ii00002i−2i−i−iii00000000-11−i−iii00000000
χ302-22-2-111-12222-2-2-2-200-1-1-11-11112-2−2i2i-22−2i−2i2i2i-112-2-1-111i−i0000−2i2iii−i−i00000000-11ii−i−i00000000
χ312-22-2-111-12222-2-2-2-200-1-1-11-1111-222i−2i-22−2i−2i2i2i1-1-2211-1-1−ii00002i−2i−i−iii00000000-11ii−i−i00000000
χ322-22-2-111-12222-2-2-2-200-1-1-11-1111-22−2i2i-222i2i−2i−2i1-1-2211-1-1i−i0000−2i2iii−i−i00000000-11−i−iii00000000
χ332-2-222-22-222-2-2-2-2220022-2-2-2-2220000002−2−22000000000000000000002-2-220000002−2−222−2−220000
χ342-2-222-22-222-2-2-2-2220022-2-2-2-2220000002−2−2200000000000000000000-222-20000002−2−22−222−20000
χ352-2-222-22-222-2-2-2-2220022-2-2-2-222000000−222−2000000000000000000002-2-22000000−222−2−222−20000
χ362-2-222-22-222-2-2-2-2220022-2-2-2-222000000−222−200000000000000000000-222-2000000−222−22−2−220000
χ37444444441-21-21-2-2144-21-2-2111-2220000000022-1-1-1-1-1-1001-21-200000000000022000000000000-1-1
χ38444444441-21-21-2-2144-21-2-2111-2-2-200000000-2-2111111001-21-2000000000000-2-200000000000011
χ39444444441-21-21-2-21-4-4-21-2-2111-2220000000022-1-1-1-1-1-100-12-12000000000000-2-200000000000011
χ40444444441-21-21-2-21-4-4-21-2-2111-2-2-200000000-2-211111100-12-1200000000000022000000000000-1-1
χ4144444444-21-21-211-2441-211-2-2-2100220000000000000022-21-21-1-1-1-1-1-1000022000000000000-1-100
χ4244444444-21-21-211-2441-211-2-2-2100-2-200000000000000-2-2-21-211111110000-2-20000000000001100
χ4344444444-21-21-211-2-4-41-211-2-2-21002200000000000000222-12-1-1-1-1-1-1-10000-2-20000000000001100
χ4444444444-21-21-211-2-4-41-211-2-2-2100-2-200000000000000-2-22-12-1111111000022000000000000-1-100
χ454444-2-2-2-24444444400-2-2-2-2-2-2-2-20000-4-40000000000000000000000000000000022000000000000
χ4644-4-4-2-22244-4-444-4-400-2-22-22-2220000002i2−2i22i2−2i2000000000000000000000000000000−i2i2−i2i200000000
χ4744-4-4-2-22244-4-444-4-400-2-22-22-222000000−2i22i2−2i22i2000000000000000000000000000000i2−i2i2−i200000000
χ484-44-44-4-441-21-2-122-14i−4i-21-221-1-122-2000000002-2-11-1-11100i−2i−i2i0000000000002i−2i000000000000−ii
χ494-44-44-4-441-21-2-122-14i−4i-21-221-1-12-2200000000-221-111-1-100i−2i−i2i000000000000−2i2i000000000000i−i
χ504-44-44-4-441-21-2-122-1−4i4i-21-221-1-122-2000000002-2-11-1-11100−i2ii−2i000000000000−2i2i000000000000i−i
χ514-44-44-4-441-21-2-122-1−4i4i-21-221-1-12-2200000000-221-111-1-100−i2ii−2i0000000000002i−2i000000000000−ii
χ524-44-44-4-44-21-212-1-124i−4i1-21-1-222-1002i−2i000000000000002i−2i−2ii2i−i−ii−i−iii00002-2000000000000-1100
χ534-44-44-4-44-21-212-1-124i−4i1-21-1-222-100−2i2i00000000000000−2i2i−2ii2i−ii−iii−i−i0000-220000000000001-100
χ544-44-44-4-44-21-212-1-12−4i4i1-21-1-222-1002i−2i000000000000002i−2i2i−i−2ii−ii−i−iii0000-220000000000001-100
χ554-44-44-4-44-21-212-1-12−4i4i1-21-1-222-100−2i2i00000000000000−2i2i2i−i−2iii−iii−i−i00002-2000000000000-1100
χ564-44-4-222-24444-4-4-4-400-2-2-22-222200004-4000000000000000000000000000000002-2000000000000
χ574-4-44-22-2244-4-4-4-44400-2-22222-2-200000022−22−2222000000000000000000000000000000−222−200000000
χ584-4-44-22-2244-4-4-4-44400-2-22222-2-2000000−222222−220000000000000000000000000000002−2−2200000000
χ598888-4-4-4-42-42-42-4-42002-122-1-1-124400000000-2-2-2-211110000000000000000000000000000000000
χ608888-4-4-4-42-42-42-4-42002-122-1-1-12-4-4000000002222-1-1-1-10000000000000000000000000000000000
χ618888-4-4-4-4-42-42-422-400-12-1-1222-1004400000000000000-2-20000-2-211110000000000000000000000
χ628888-4-4-4-4-42-42-422-400-12-1-1222-100-4-40000000000000022000022-1-1-1-10000000000000000000000
χ6388-8-888-8-82-4-242-44-200-424-4-22-240000000000000000000000000000000000000000000000000000
χ6488-8-888-8-8-424-2-42-24002-4-224-44-20000000000000000000000000000000000000000000000000000
χ6588-8-8-4-4442-4-242-44-2002-1-221-11-2000000000000003-33-30000000000000000000000000000000000
χ6688-8-8-4-4442-4-242-44-2002-1-221-11-200000000000000-33-330000000000000000000000000000000000
χ6788-8-8-4-444-424-2-42-2400-121-1-22-21000000000000000000000000003i−3i3i−3i0000000000000000000000
χ6888-8-8-4-444-424-2-42-2400-121-1-22-2100000000000000000000000000−3i3i−3i3i0000000000000000000000
χ698-88-8-444-42-42-4-244-2002-12-2-111-24-400000000-22-2211-1-10000000000000000000000000000000000
χ708-88-8-444-42-42-4-244-2002-12-2-111-2-44000000002-22-2-1-1110000000000000000000000000000000000
χ718-88-8-444-4-42-424-2-2400-12-112-2-21004i−4i00000000000000−2i2i0000−2i2iii−i−i0000000000000000000000
χ728-88-8-444-4-42-424-2-2400-12-112-2-2100−4i4i000000000000002i−2i00002i−2i−i−iii0000000000000000000000
χ738-8-888-88-82-4-24-24-4200-4244-2-22-40000000000000000000000000000000000000000000000000000
χ748-8-888-88-8-424-24-22-4002-4-2-244-420000000000000000000000000000000000000000000000000000
χ758-8-88-44-442-4-24-24-42002-1-2-211-12000000000000003-3-330000000000000000000000000000000000
χ768-8-88-44-442-4-24-24-42002-1-2-211-1200000000000000-333-30000000000000000000000000000000000
χ778-8-88-44-44-424-24-22-400-1211-2-22-1000000000000000000000000003-3-330000000000000000000000
χ788-8-88-44-44-424-24-22-400-1211-2-22-100000000000000000000000000-333-30000000000000000000000

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