Finite Group Databasebeta

← Group #11785800

Character table — Group #11785800

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444444444448888888899991212121212121212121212121212121218181818242424242424242424242424242424243672727272
order12222244334666666666612121212661212121212122222444444448888888822441212121212121212242424242424242444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1iiii−i−i−i−i1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−i−i−iiiii1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111-1-1-1-11111iiii−i−i−i−i1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111-1-1-1-11111−i−i−i−iiiii1ii−i−i
χ91111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-11-11-1
χ101111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-1-111-1-11-11
χ111111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1-1-111-1-111-1-11111-1-111-1-1-1-11-11
χ121111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-11-11-1
χ131111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111ii−i−i−i−iii111111-1-1-1-111ii−i−i−i−iii-1i−i−ii
χ141111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111−i−iiiii−i−i111111-1-1-1-111−i−iiiii−i−i-1−iii−i
χ151111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1ii−i−i−i−iii1111-1-11111-1-1ii−i−i−i−iii-1−iii−i
χ161111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−iiiii−i−i1111-1-11111-1-1−i−iiiii−i−i-1i−i−ii
χ17222222222222222222222222222222222-2-2-2-20000000000000000-2-2-2-20000000000000000-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-22222000000000000000022-2-20000000000000000-20000
χ192222-2-22222-2222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000000000000022-2-2000000000000000020000
χ202222-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2000000000000000020000
χ2122-2-22-20022022-222-2-2-2-2-200002-200000022-2-2000000002−22−22−22−22-200000000002−22−22−22−200000
χ2222-2-22-20022022-222-2-2-2-2-200002-200000022-2-200000000−22−22−22−222-20000000000−22−22−22−2200000
χ2322-2-22-20022022-222-2-2-2-2-200002-2000000-2-22200000000i2−i2i2−i2−i2i2−i2i2-220000000000i2−i2i2−i2−i2i2−i2i200000
χ2422-2-22-20022022-222-2-2-2-2-200002-2000000-2-22200000000−i2i2−i2i2i2−i2i2−i2-220000000000−i2i2−i2i2i2−i2i2−i200000
χ2522-2-2-220022022-2-2-222-2-2-20000-2200000022-2-2000000002−2−222−2−22-2200000000002−2−222−2−2200000
χ2622-2-2-220022022-2-2-222-2-2-20000-2200000022-2-200000000−222−2−222−2-220000000000−222−2−222−200000
χ2722-2-2-220022022-2-2-222-2-2-20000-22000000-2-22200000000i2−i2−i2i2−i2i2i2−i22-20000000000i2−i2−i2i2−i2i2i2−i200000
χ2822-2-2-220022022-2-2-222-2-2-20000-22000000-2-22200000000−i2i2i2−i2i2−i2−i2i22-20000000000−i2i2i2−i2i2−i2−i2i200000
χ292-22-2002-2220-2-2-2000022-222-2-2002-200002-22-2002i−2i002i−2i00000000002-2002i−2i002i−2i0000000000000
χ302-22-2002-2220-2-2-2000022-222-2-2002-200002-22-200−2i2i00−2i2i00000000002-200−2i2i00−2i2i0000000000000
χ312-22-2002-2220-2-2-2000022-222-2-2002-20000-22-222i−2i002i−2i000000000000-222i−2i002i−2i000000000000000
χ322-22-2002-2220-2-2-2000022-222-2-2002-20000-22-22−2i2i00−2i2i000000000000-22−2i2i00−2i2i000000000000000
χ332-22-200-22220-2-2-2000022-2-2-22200-2200002-22-22i−2i00−2i2i000000000000-222i−2i00−2i2i000000000000000
χ342-22-200-22220-2-2-2000022-2-2-22200-2200002-22-2−2i2i002i−2i000000000000-22−2i2i002i−2i000000000000000
χ352-22-200-22220-2-2-2000022-2-2-22200-220000-22-22002i−2i00−2i2i00000000002-2002i−2i00−2i2i0000000000000
χ362-22-200-22220-2-2-2000022-2-2-22200-220000-22-2200−2i2i002i−2i00000000002-200−2i2i002i−2i0000000000000
χ37444444441-241-21-2-2-2-21-2-2111111-2-211-2-200000000000022222222000000000000-1-1-1-1-1-1-1-100000
χ38444444441-241-21-2-2-2-21-2-2111111-2-211-2-2000000000000-2-2-2-2-2-2-2-20000000000001111111100000
χ3944444444-214-21-21111-211-2-2-2-2-2-211-2-211000022222222000000000000-1-1-1-1-1-1-1-10000000000000
χ4044444444-214-21-21111-211-2-2-2-2-2-211-2-2110000-2-2-2-2-2-2-2-2000000000000111111110000000000000
χ41444444-4-41-2-41-21-2-2-2-21-2-2-1-1-1-11122-1-1220000000000002i2i2i2i−2i−2i−2i−2i000000000000−i−i−i−iiiii00000
χ42444444-4-41-2-41-21-2-2-2-21-2-2-1-1-1-11122-1-122000000000000−2i−2i−2i−2i2i2i2i2i000000000000iiii−i−i−i−i00000
χ43444444-4-4-21-4-21-21111-2112222-2-2-1-122-1-100002222-2-2-2-2000000000000-1-1-1-111110000000000000
χ44444444-4-4-21-4-21-21111-2112222-2-2-1-122-1-10000-2-2-2-222220000000000001111-1-1-1-10000000000000
χ454444-4-4441-2-41-2122221-2-21111-1-1-2-2-1-12200000000000022-2-222-2-2000000000000-1-111-1-11100000
χ464444-4-4441-2-41-2122221-2-21111-1-1-2-2-1-122000000000000-2-222-2-22200000000000011-1-111-1-100000
χ474444-4-444-21-4-21-2-1-1-1-1-211-2-2-2-2221122-1-1000022-2-222-2-2000000000000-1-111-1-1110000000000000
χ484444-4-444-21-4-21-2-1-1-1-1-211-2-2-2-2221122-1-10000-2-222-2-22200000000000011-1-111-1-10000000000000
χ494444-4-4-4-41-241-2122221-2-2-1-1-1-1-1-12211-2-20000000000002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i00000
χ504444-4-4-4-41-241-2122221-2-2-1-1-1-1-1-12211-2-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii00000
χ514444-4-4-4-4-214-21-2-1-1-1-1-211222222-1-1-2-211000022-2-2-2-222000000000000-1-11111-1-10000000000000
χ524444-4-4-4-4-214-21-2-1-1-1-1-211222222-1-1-2-2110000-2-22222-2-200000000000011-1-1-1-1110000000000000
χ5344-4-44-4001-201-2-1-2-222-1223i−3i3i−3i1-1003i−3i000000000000002ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3000000000000−ζζ−ζζζ3−ζ3ζ3−ζ300000
χ5444-4-44-4001-201-2-1-2-222-1223i−3i3i−3i1-1003i−3i00000000000000−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3000000000000ζ−ζζ−ζ−ζ3ζ3−ζ3ζ300000
χ5544-4-44-4001-201-2-1-2-222-122−3i3i−3i3i1-100−3i3i000000000000002ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ000000000000−ζ3ζ3−ζ3ζ3ζ−ζζ−ζ00000
χ5644-4-44-4001-201-2-1-2-222-122−3i3i−3i3i1-100−3i3i00000000000000−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ000000000000ζ3−ζ3ζ3−ζ3−ζζ−ζζ00000
χ5744-4-4-44001-201-2-122-2-2-1223i−3i3i−3i-1100−3i3i000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000−ζζζ−ζζ3−ζ3−ζ3ζ300000
χ5844-4-4-44001-201-2-122-2-2-1223i−3i3i−3i-1100−3i3i00000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000ζ−ζ−ζζ−ζ3ζ3ζ3−ζ300000
χ5944-4-4-44001-201-2-122-2-2-122−3i3i−3i3i-11003i−3i000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000−ζ3ζ3ζ3−ζ3ζ−ζ−ζζ00000
χ6044-4-4-44001-201-2-122-2-2-122−3i3i−3i3i-11003i−3i00000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000ζ3−ζ3−ζ3ζ3−ζζζ−ζ00000
χ614-44-4004-4-2102-123-33-3-21-1-2-222001-1003-300002i−2i2i−2i2i−2i2i−2i000000000000−ii−ii−ii−ii0000000000000
χ624-44-4004-4-2102-123-33-3-21-1-2-222001-1003-30000−2i2i−2i2i−2i2i−2i2i000000000000i−ii−ii−ii−i0000000000000
χ634-44-4004-4-2102-12-33-33-21-1-2-222001-100-3300002i−2i−2i2i2i−2i−2i2i000000000000−iii−i−iii−i0000000000000
χ644-44-4004-4-2102-12-33-33-21-1-2-222001-100-330000−2i2i2i−2i−2i2i2i−2i000000000000i−i−iii−i−ii0000000000000
χ654-44-400-44-2102-123-33-3-21-122-2-200-1100-3300002i−2i2i−2i−2i2i−2i2i000000000000−ii−iii−ii−i0000000000000
χ664-44-400-44-2102-123-33-3-21-122-2-200-1100-330000−2i2i−2i2i2i−2i2i−2i000000000000i−ii−i−ii−ii0000000000000
χ674-44-400-44-2102-12-33-33-21-122-2-200-11003-300002i−2i−2i2i−2i2i2i−2i000000000000−iii−ii−i−ii0000000000000
χ684-44-400-44-2102-12-33-33-21-122-2-200-11003-30000−2i2i2i−2i2i−2i−2i2i000000000000i−i−ii−iii−i0000000000000
χ694-4-440000440-4-440000-4-440000000000004-4-4400000000000000000000000000000000000000000
χ704-4-440000440-4-440000-4-44000000000000-444-400000000000000000000000000000000000000000
χ7188-8-88-800-420-42422-2-24-2-20000-44000000000000000000000000000000000000000000000000000
χ7288-8-8-8800-420-424-2-2224-2-200004-4000000000000000000000000000000000000000000000000000
χ738-88-8008-82-40-24-200002-4422-2-200-440000000000000000000000000000000000000000000000000
χ748-88-800-882-40-24-200002-44-2-222004-40000000000000000000000000000000000000000000000000
χ758-8-8800002-40-2420000-24-46i−6i−6i6i00000000000000000000000000000000000000000000000000000
χ768-8-8800002-40-2420000-24-4−6i6i6i−6i00000000000000000000000000000000000000000000000000000
χ778-8-880000-4204-2-46-6-664-22000000000000000000000000000000000000000000000000000000000
χ788-8-880000-4204-2-4-666-64-22000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.