Finite Group Databasebeta

← Group #13139175

Character table — Group #13139175

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order124423461212688122424242433661212121236661212121222446612126122424242424242424688888888881224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111-1-11-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111-1-11-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ711111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1111111-1-1
χ811111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-111111111-1-1-1-1-1-111
χ911-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-11-1-11-1-1111-11-111-1-1-11ii−i−iii−i−i-1i−ii−ii−i1-11-11ii−i−i11-1-111-1-1i−ii−i
χ1011-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-11-1-11-1-1111-11-111-1-1-11ii−i−iii−i−i-1i−i−ii−ii-11-111ii−i−i-1-111-1-111−ii−ii
χ1111-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-11-1-11-1-111-11-11-1-111-11ii−i−iii−i−i1−iii−i−ii1-1-11-1−i−iii11-1-1-1-111i−i−ii
χ1211-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-11-1-11-1-111-11-11-1-111-11ii−i−iii−i−i1−ii−iii−i-111-1-1−i−iii-1-11111-1-1−iii−i
χ1311-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-11-1-11-1-1111-11-111-1-1-11−i−iii−i−iii-1−iii−ii−i-11-111−i−iii-1-111-1-111i−ii−i
χ1411-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-11-1-11-1-1111-11-111-1-1-11−i−iii−i−iii-1−ii−ii−ii1-11-11−i−iii11-1-111-1-1−ii−ii
χ1511-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-11-1-11-1-111-11-11-1-111-11−i−iii−i−iii1i−ii−i−ii-111-1-1ii−i−i-1-11111-1-1i−i−ii
χ1611-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-11-1-11-1-111-11-11-1-111-11−i−iii−i−iii1i−i−iii−i1-1-11-1ii−i−i11-1-1-1-111−iii−i
χ172222222222222222222-12-122-1-1-12-1-1-1-12-100000000-1-12-12-1-1-1-1-100000220022000000000-1-1-1-100-1-1
χ182222222222222222222-12-122-1-1-12-1-1-1-12-100000000-1-12-12-1-1-1-1-100000-2-200-2-200000000011110011
χ19222222222222222222-12-12-1-122-1-12-1-1-1-1200000000-1-1-12-12-1-1-1-10002200220000000-1-1-1-10000-1-100
χ20222222222222222222-12-12-1-122-1-12-1-1-1-1200000000-1-1-12-12-1-1-1-1000-2-200-2-20000000111100001100
χ2122222222222-2-22-2-2-2-22-12-122-1-1-12-1-1-1-12-100000000-1-1-21-211111000002200-2-2000000000111100-1-1
χ2222222222222-2-22-2-2-2-22-12-122-1-1-12-1-1-1-12-100000000-1-1-21-21111100000-2-20022000000000-1-1-1-10011
χ2322222222222-2-22-2-2-2-2-12-12-1-122-1-12-1-1-1-1200000000-1-11-21-211110002200-2-2000000011110000-1-100
χ2422222222222-2-22-2-2-2-2-12-12-1-122-1-12-1-1-1-1200000000-1-11-21-21111000-2-200220000000-1-1-1-100001100
χ252222-22-2222-200-20000222222222-2-2222-2-22-2-222222-2-200000000-20000000000-20000000000000000
χ262222-22-2222-200-20000222222222-2-2222-2-2-222-2-2-2-2-2-2-2000000002000000000020000000000000000
χ2722-2-222-22-2-2200-200002222-2-2-2-22222-2-2-2-222-2-222-2-22-20000000020000000000-20000000000000000
χ2822-2-222-22-2-2200-200002222-2-2-2-22222-2-2-2-2-2-222-2-2222-200000000-2000000000020000000000000000
χ2922-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-1-2-211-1-21-1112-1000000001-12i−i−2ii−i−iii000002i−2i002-2000000000-1-11100−ii
χ3022-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-1-2-211-1-21-1112-1000000001-12i−i−2ii−i−iii00000−2i2i00-2200000000011-1-100i−i
χ3122-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-1211-2-2-11-2-111-12000000001-1−i2ii−2i−i−iii0002i−2i002-20000000-1-1110000−ii00
χ3222-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-1211-2-2-11-2-111-12000000001-1−i2ii−2i−i−iii000−2i2i00-22000000011-1-10000i−i00
χ3322-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-1-2-211-1-21-1112-1000000001-1−2ii2i−iii−i−i000002i−2i00-2200000000011-1-100−ii
χ3422-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-1-2-211-1-21-1112-1000000001-1−2ii2i−iii−i−i00000−2i2i002-2000000000-1-11100i−i
χ3522-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-1211-2-2-11-2-111-12000000001-1i−2i−i2iii−i−i0002i−2i00-22000000011-1-10000−ii00
χ3622-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-1211-2-2-11-2-111-12000000001-1i−2i−i2iii−i−i000−2i2i002-20000000-1-1110000i−i00
χ37444444444444444444-2-2-2-2-2-2-2-21-2-2111-2-20000000011-2-2-2-211110000000000000000000000000000
χ3844444444444-4-44-4-4-4-4-2-2-2-2-2-2-2-21-2-2111-2-200000000112222-1-1-1-10000000000000000000000000000
χ394444-44-4444-400-400004-24-244-2-2-2-42-2-2-2-420000000022000000000000000000000000000000000000
χ404444-44-4444-400-40000-24-24-2-244-22-4-2-2-22-40000000022000000000000000000000000000000000000
χ414444-44-4444-400-40000-2-2-2-2-2-2-2-21221112200000000-1-100003-33-30000000000000000000000000000
χ424444-44-4444-400-40000-2-2-2-2-2-2-2-21221112200000000-1-10000-33-330000000000000000000000000000
χ4344-4-444-44-4-4400-400004-24-2-4-422-24-2-222-4200000000-22000000000000000000000000000000000000
χ4444-4-444-44-4-4400-40000-24-2422-4-4-2-24-2222-400000000-22000000000000000000000000000000000000
χ4544-4-444-44-4-4400-40000-2-2-2-222221-2-21-1-122000000001-100003i−3i−3i3i0000000000000000000000000000
χ4644-4-444-44-4-4400-40000-2-2-2-222221-2-21-1-122000000001-10000−3i3i3i−3i0000000000000000000000000000
χ4744-4-4-4444-4-4-44i−4i44i4i−4i−4i-2-2-2-222221221-1-1-2-200000000-11−2i−2i2i2iii−i−i0000000000000000000000000000
χ4844-4-4-4444-4-4-4−4i4i4−4i−4i4i4i-2-2-2-222221221-1-1-2-200000000-112i2i−2i−2i−i−iii0000000000000000000000000000
χ494-44i−4i040-44i−4i0000000044-4-44i−4i4i−4i400-44i−4i000000000000000000000000000000000000000000000000
χ504-44i−4i040-44i−4i000000004-2-424i−4i−2i2i-2002−2i2i00000000000000000000000000000000000000006−6i6−i60000
χ514-44i−4i040-44i−4i000000004-2-424i−4i−2i2i-2002−2i2i0000000000000000000000000000000000000000−66−i6i60000
χ524-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i-2002−2i2i000000000000000000000000000000000000i6−i66−600000000
χ534-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i-2002−2i2i000000000000000000000000000000000000−i6i6−6600000000
χ544-4−4i4i040-4−4i4i0000000044-4-4−4i4i−4i4i400-4−4i4i000000000000000000000000000000000000000000000000
χ554-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i-20022i−2i00000000000000000000000000000000000000006−6−i6i60000
χ564-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i-20022i−2i0000000000000000000000000000000000000000−66i6−i60000
χ574-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i-20022i−2i000000000000000000000000000000000000i6−i6−6600000000
χ584-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i-20022i−2i000000000000000000000000000000000000−i6i66−600000000
χ5966666-36-3-3-3-366-3-3-3-3-300000000000000002222-1-1-1-10000000000-12200000000-1-1-1-1-1000000000000
χ6066666-36-3-3-3-366-3-3-3-3-30000000000000000-2-2-2-2111100000000001-2-20000000011111000000000000
χ6166666-36-3-3-3-3-6-6-3333300000000000000002222-1-1-1-10000000000-1-2-200000000-11111000000000000
χ6266666-36-3-3-3-3-6-6-333330000000000000000-2-2-2-211110000000000122000000001-1-1-1-1000000000000
χ636666-6-3-6-3-3-33003−3i33i3−3i33i300000000000000002-2-22-1-1-1-10000000000100000000001−i3i3−i3i3000000000000
χ646666-6-3-6-3-3-33003−3i33i3−3i33i30000000000000000-222-211110000000000-10000000000-1i3−i3i3−i3000000000000
χ656666-6-3-6-3-3-330033i3−3i33i3−3i300000000000000002-2-22-1-1-1-10000000000100000000001i3−i3i3−i3000000000000
χ666666-6-3-6-3-3-330033i3−3i33i3−3i30000000000000000-222-211110000000000-10000000000-1−i3i3−i3i3000000000000
χ6766-6-66-3-6-333-300333−33−3333000000000000000022-2-2-1-1110000000000-1000000000013−3−33000000000000
χ6866-6-66-3-6-333-300333−33−33330000000000000000-2-22211-1-1000000000010000000000-1−333−3000000000000
χ6966-6-66-3-6-333-3003−333333−33000000000000000022-2-2-1-1110000000000-100000000001−333−3000000000000
χ7066-6-66-3-6-333-3003−333333−330000000000000000-2-22211-1-1000000000010000000000-13−3−33000000000000
χ7166-6-6-6-36-33336i−6i-3−3i−3i3i3i00000000000000002-22-2-1-111000000000012i−2i00000000-1−i−iii000000000000
χ7266-6-6-6-36-33336i−6i-3−3i−3i3i3i0000000000000000-22-2211-1-10000000000-1−2i2i000000001ii−i−i000000000000
χ7366-6-6-6-36-3333−6i6i-33i3i−3i−3i00000000000000002-22-2-1-11100000000001−2i2i00000000-1ii−i−i000000000000
χ7466-6-6-6-36-3333−6i6i-33i3i−3i−3i0000000000000000-22-2211-1-10000000000-12i−2i000000001−i−iii000000000000
χ758-88i−8i080-88i−8i00000000-4-444−4i4i−4i4i200-22i−2i000000000000000000000000000000000000000000000000
χ768-8−8i8i080-8−8i8i00000000-4-4444i−4i4i−4i200-2−2i2i000000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i0000000000000000000000000000−2i32i323−2300000000000000000000000000000000000000
χ7812-1212i−12i0-606−6i6i00000000000000000000000000002i3−2i3−232300000000000000000000000000000000000000
χ7912-12−12i12i0-6066i−6i0000000000000000000000000000−2i32i3−232300000000000000000000000000000000000000
χ8012-12−12i12i0-6066i−6i00000000000000000000000000002i3−2i323−2300000000000000000000000000000000000000

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