Finite Group Databasebeta

← Group #72220485

Character table — Group #72220485

Order 6912.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222448899161616181818242424243232363648484848484848484848545472727272969696969696108108108144144144144144144144144144144216216216216216216216216216216288288288288
order12244223622612122443666662236666666121244666666661212444666688881212448888888824242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111-1-111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ411111-1-111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ5111-1-11-111111-1-11-1-111111-11-1111-1-1111-1-111111111-1-1-1-11-1-111-1-1i−ii−i-1-11-1ii−i−iii−i−ii−ii−i
χ6111-1-11-111111-1-11-1-111111-11-1111-1-1111-1-111111111-1-1-1-11-1-111-1-1−ii−ii-1-11-1−i−iii−i−iii−ii−ii
χ7111-1-1-1111111-1-11-1-11111-11-111-1-111111-1-1111111-1-111-1-11-1-1-1-111i−i−ii-1-1-11ii−i−i−i−iiii−i−ii
χ8111-1-1-1111111-1-11-1-11111-11-111-1-111111-1-1111111-1-111-1-11-1-1-1-111−iii−i-1-1-11−i−iiiii−i−i−iii−i
χ922222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1222-1-1-1-10000-1-122000000000000
χ10222222222-2-2222-2-2-2-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1001111-1-1-1-1-1-1000111100001100−i2i2−i2i2−i2i2−i2i20000
χ11222222222-2-2222-2-2-2-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1001111-1-1-1-1-1-1000111100001100i2−i2i2−i2i2−i2i2−i20000
χ1222222-2-22222222222-1-1-1-1-2-2-2-2-11111-1-1-1-1-122-1-1-1-11111-1-122211110000-1-1-2-2000000000000
χ1322222-2-222-2-2222-2-2-2-1-1-1-1-2-222-11111-1-1-1-1-10011111111-1-1000-1-1-1-100001100−i2i2−i2i2i2−i2i2−i20000
χ1422222-2-222-2-2222-2-2-2-1-1-1-1-2-222-11111-1-1-1-1-10011111111-1-1000-1-1-1-100001100i2−i2i2−i2−i2i2−i2i20000
χ15222-2-22-222222-2-22-2-2-1-1-1-12-22-2-1-1-111-1-1-11122-1-1-1-1-1-111112-2-2-1-1110000112-2000000000000
χ16222-2-22-222-2-22-2-2-222-1-1-1-12-2-22-1-1-111-1-1-111001111-1-1111100011-1-10000-1-1002−2−222−2−220000
χ17222-2-22-222-2-22-2-2-222-1-1-1-12-2-22-1-1-111-1-1-111001111-1-1111100011-1-10000-1-100−222−2−222−20000
χ18222-2-2-2222222-2-22-2-2-1-1-1-1-22-22-111-1-1-1-1-11122-1-1-1-111-1-1112-2-211-1-1000011-22000000000000
χ19222-2-2-2222-2-22-2-2-222-1-1-1-1-222-2-111-1-1-1-1-11100111111-1-111000-1-1110000-1-1002−2−22−222−20000
χ20222-2-2-2222-2-22-2-2-222-1-1-1-1-222-2-111-1-1-1-1-11100111111-1-111000-1-1110000-1-100−222−22−2−220000
χ2122-22-2002222-22-2-22-22-2-22000020000-2-222-22222-2-200002-2-22-2000000002-200000000000000
χ2222-22-2002222-22-2-22-2-111-10000-1−i3i3−i3i311-1-1122-1-111−i3i3−i3i3-11-22-2−i3i3−i3i30000-1100000000000000
χ2322-22-2002222-22-2-22-2-111-10000-1i3−i3i3−i311-1-1122-1-111i3−i3i3−i3-11-22-2i3−i3i3−i30000-1100000000000000
χ2422-2-22002222-2-22-2-222-2-22000020000-2-22-222222-2-20000-22-2-2200000000-2200000000000000
χ2522-2-22002222-2-22-2-22-111-10000-1−i3i3i3−i311-11-122-1-111−i3i3i3−i31-1-2-22−i3i3i3−i300001-100000000000000
χ2622-2-22002222-2-22-2-22-111-10000-1i3−i3−i3i311-11-122-1-111i3−i3−i3i31-1-2-22i3−i3−i3i300001-100000000000000
χ2733333333333333333000033330000000000-1-10000000000-1-1-10000111100-1-1-1-1-1-1-1-1-1-11111
χ2833333333333333333000033330000000000-1-10000000000-1-1-10000-1-1-1-100-1-111111111-1-1-1-1
χ2933333-3-333333333330000-3-3-3-30000000000-1-10000000000-1-1-1000011-1-10011-1-1-1-1111111-1-1
χ3033333-3-333333333330000-3-3-3-30000000000-1-10000000000-1-1-10000-1-11100111111-1-1-1-1-1-111
χ31333-3-33-333333-3-33-3-300003-33-30000000000-1-10000000000-1110000i−ii−i00-11−i−iii−i−iiii−ii−i
χ32333-3-33-333333-3-33-3-300003-33-30000000000-1-10000000000-1110000−ii−ii00-11ii−i−iii−i−i−ii−ii
χ33333-3-3-3333333-3-33-3-30000-33-330000000000-1-10000000000-1110000i−i−ii001-1−i−iiiii−i−ii−i−ii
χ34333-3-3-3333333-3-33-3-30000-33-330000000000-1-10000000000-1110000−iii−i001-1ii−i−i−i−iii−iii−i
χ35444444444-4-4444-4-4-4111144-4-4111111111100-1-1-1-1111111000-1-1-1-10000-1-100000000000000
χ3644444-4-444-4-4444-4-4-41111-4-4441-1-1-1-11111100-1-1-1-1-1-1-1-11100011110000-1-100000000000000
χ37444-4-44-444-4-44-4-4-44411114-4-44111-1-1111-1-100-1-1-1-111-1-1-1-1000-1-11100001100000000000000
χ38444-4-4-4444-4-44-4-4-4441111-444-41-1-111111-1-100-1-1-1-1-1-111-1-100011-1-100001100000000000000
χ3944-44-40044-4-4-44-44-441-1-1100001−i3i3−i3i3-1-111-100-1-111−i3i3−i3i31-1000i3−i3i3−i30000-1100000000000000
χ4044-44-40044-4-4-44-44-441-1-1100001i3−i3i3−i3-1-111-100-1-111i3−i3i3−i31-1000−i3i3−i3i30000-1100000000000000
χ4144-44-40044-4-4-44-44-44-222-20000-2000022-2-220022-2-20000-22000000000002-200000000000000
χ4244-4-440044-4-4-4-4444-41-1-1100001−i3i3i3−i3-1-11-1100-1-111−i3i3i3−i3-11000i3−i3−i3i300001-100000000000000
χ4344-4-440044-4-4-4-4444-41-1-1100001i3−i3−i3i3-1-11-1100-1-111i3−i3−i3i3-11000−i3i3i3−i300001-100000000000000
χ4444-4-440044-4-4-4-4444-4-222-20000-2000022-22-20022-2-200002-200000000000-2200000000000000
χ454-4000004-4-44000000400-400004000000-4004-44-400000000000000000000000000000000000
χ464-4000004-4-44000000-2−2i32i320000-20000−2i32i32004-4-22−2i32i3000000000000000000000000000000000
χ474-4000004-4-44000000-22i3−2i320000-200002i3−2i32004-4-222i3−2i3000000000000000000000000000000000
χ4866-66-6006666-66-6-66-6000000000000000000-2-200000000002-22000000000000000000000000
χ4966-6-66006666-6-66-6-66000000000000000000-2-2000000000022-2000000000000000000000000
χ508888888-1-100-1-1-10002222-1-100-12222-1-1-122000000-1-1-1-1-1-100000002222000000000000-1-1-1-1
χ518888888-1-100-1-1-10002222-1-100-12222-1-1-122000000-1-1-1-1-1-10000000-2-2-2-20000000000001111
χ5288888-8-8-1-100-1-1-100022221100-1-2-2-2-2-1-1-1220000001111-1-1000000022-2-2000000000000-1-111
χ5388888-8-8-1-100-1-1-100022221100-1-2-2-2-2-1-1-1220000001111-1-10000000-2-22200000000000011-1-1
χ54888-8-88-8-1-100-1110002222-1100-122-2-2-1-1-1-2-2000000-1-1111100000002i−2i2i−2i000000000000−ii−ii
χ55888-8-88-8-1-100-1110002222-1100-122-2-2-1-1-1-2-2000000-1-111110000000−2i2i−2i2i000000000000i−ii−i
χ56888-8-8-88-1-100-11100022221-100-1-2-222-1-1-1-2-200000011-1-11100000002i−2i−2i2i000000000000−iii−i
χ57888-8-8-88-1-100-11100022221-100-1-2-222-1-1-1-2-200000011-1-1110000000−2i2i2i−2i000000000000i−i−ii
χ588-8000008-88-80000002−2i32i3-2000020000−2i32i3-20000-222i3−2i3000000000000000000000000000000000
χ598-8000008-88-800000022i3−2i3-20000200002i3−2i3-20000-22−2i32i3000000000000000000000000000000000
χ608-8000008-88-8000000-40040000-4000000400004-400000000000000000000000000000000000
χ6112-120000012-12-1212000000000000000000000000-440000000000000000000000000000000000000
χ6216161616161616-2-200-2-2-2000-2-2-2-2-2-2001-2-2-2-2111-2-2000000111111000000000000000000000000000
χ631616161616-16-16-2-200-2-2-2000-2-2-2-2220012222111-2-2000000-1-1-1-111000000000000000000000000000
χ64161616-16-1616-16-2-200-222000-2-2-2-2-22001-2-2221112200000011-1-1-1-1000000000000000000000000000
χ65161616-16-16-1616-2-200-222000-2-2-2-22-200122-2-211122000000-1-111-1-1000000000000000000000000000
χ661616-1616-1600-2-2002-220004-4-440000-2000022-24-40000000000-22000000000000000000000000000
χ671616-1616-1600-2-2002-22000-222-200001−2i32i3−2i32i3-1-11-22000000i3−i3i3−i31-1000000000000000000000000000
χ681616-1616-1600-2-2002-22000-222-2000012i3−2i32i3−2i3-1-11-22000000−i3i3−i3i31-1000000000000000000000000000
χ691616-16-161600-2-20022-20004-4-440000-2000022-2-4400000000002-2000000000000000000000000000
χ701616-16-161600-2-20022-2000-222-200001−2i32i32i3−2i3-1-112-2000000i3−i3−i3i3-11000000000000000000000000000
χ711616-16-161600-2-20022-2000-222-2000012i3−2i3−2i32i3-1-112-2000000−i3i3i3−i3-11000000000000000000000000000
χ7232-3200000-4400000000800-80000-4000000400000000000000000000000000000000000000000
χ7332-3200000-4400000000-4−4i34i340000200002i3−2i3-200000000000000000000000000000000000000000
χ7432-3200000-4400000000-44i3−4i34000020000−2i32i3-200000000000000000000000000000000000000000

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