Finite Group Databasebeta

← Group #10591007

Character table — Group #10591007

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11222222222334444444444444446666666888888881212121212121212121212122424242436363636
order12233446612124436668812121212122424242422466121261224242424242444688881224242424121224242288
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-111111-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-1-111-1-1
χ411111111111111111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-111
χ511111111111-1-1111111111111111-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ611111111111-1-1111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1-1111111-1-1-1-111
χ811111111111-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-11111-1-11111-1-1
χ911111-1-111-1-1111111i−i-1-1-1-1-1ii−i−i-1-11-1-1111-1iii−i−i−i1-1-1i−ii−i1ii−i−i1-1i−i1-1i−i
χ1011111-1-111-1-1111111i−i-1-1-1-1-1ii−i−i-1-11-1-1111-1iii−i−i−i-11-1i−i−ii1ii−i−i-11−ii-11−ii
χ1111111-1-111-1-1111111−ii-1-1-1-1-1−i−iii-1-11-1-1111-1−i−i−iiii1-1-1−ii−ii1−i−iii1-1−ii1-1−ii
χ1211111-1-111-1-1111111−ii-1-1-1-1-1−i−iii-1-11-1-1111-1−i−i−iiii-11-1−iii−i1−i−iii-11i−i-11i−i
χ1311111-1-111-1-1-1-11111i−i-1-1-1-1-1ii−i−i11-111-1-11-1iii−i−i−i1-11−iii−i-1−i−iii1-1i−i-11−ii
χ1411111-1-111-1-1-1-11111i−i-1-1-1-1-1ii−i−i11-111-1-11-1iii−i−i−i-111−ii−ii-1−i−iii-11−ii1-1i−i
χ1511111-1-111-1-1-1-11111−ii-1-1-1-1-1−i−iii11-111-1-11-1−i−i−iiii1-11i−i−ii-1ii−i−i1-1−ii-11i−i
χ1611111-1-111-1-1-1-11111−ii-1-1-1-1-1−i−iii11-111-1-11-1−i−i−iiii-111i−ii−i-1ii−i−i-11i−i1-1−ii
χ172222-122-12-1-122-12-1-122-12-1-12-1-1-1-1222-1-1-1-1-1-12-1-12-1-100-12200-1-1-1-1-100000000
χ182222-122-12-1-122-12-1-1-2-2-12-1-121111222-1-1-1-1-1-1-211-21100-1-2-200-1111100000000
χ192222-122-12-1-1-2-2-12-1-122-12-1-12-1-1-1-1-2-2-21111-1-12-1-12-1-1001-2-2001111100000000
χ202222-122-12-1-1-2-2-12-1-1-2-2-12-1-121111-2-2-21111-1-1-211-21100122001-1-1-1-100000000
χ212222-1-2-2-121122-12-1-12i−2i1-211-2−i−iii-2-2211-1-1-112i−i−i−2iii0012i−2i00-1−i−iii00000000
χ222222-1-2-2-121122-12-1-1−2i2i1-211-2ii−i−i-2-2211-1-1-11−2iii2i−i−i001−2i2i00-1ii−i−i00000000
χ232222-1-2-2-1211-2-2-12-1-12i−2i1-211-2−i−iii22-2-1-111-112i−i−i−2iii00-1−2i2i001ii−i−i00000000
χ242222-1-2-2-1211-2-2-12-1-1−2i2i1-211-2ii−i−i22-2-1-111-11−2iii2i−i−i00-12i−2i001−i−iii00000000
χ25222-12222-12200-1-12-1222-1-1-1-122220000000-1-1-1-1-1-1-1-1220002200000-1-1-1-10000
χ26222-12222-12200-1-12-1222-1-1-1-122220000000-1-1-1-1-1-1-1-1-2-2000-2-20000011110000
χ27222-12222-12200-1-12-1-2-22-1-1-1-1-2-2-2-20000000-1-111111122000-2-200000-1-1110000
χ28222-12222-12200-1-12-1-2-22-1-1-1-1-2-2-2-20000000-1-1111111-2-2000220000011-1-10000
χ29222-12-2-22-1-2-200-1-12-12i−2i-211112i2i−2i−2i0000000-11−i−i−iiii2-20002i−2i00000-11−ii0000
χ30222-12-2-22-1-2-200-1-12-12i−2i-211112i2i−2i−2i0000000-11−i−i−iiii-22000−2i2i000001-1i−i0000
χ31222-12-2-22-1-2-200-1-12-1−2i2i-21111−2i−2i2i2i0000000-11iii−i−i−i2-2000−2i2i00000-11i−i0000
χ32222-12-2-22-1-2-200-1-12-1−2i2i-21111−2i−2i2i2i0000000-11iii−i−i−i-220002i−2i000001-1−ii0000
χ3322-2222-22222222-2-2200-2222-200002-2-22222-2-200000000-20000-2000000000000
χ3422-2222-22222-2-22-2-2200-2222-20000-222-2-2-2-2-2-200000000200002000000000000
χ3522-222-2222-2-2222-2-22002-2-2-220000-22-2-2-222-220000000020000-2000000000000
χ3622-222-2222-2-2-2-22-2-22002-2-2-2200002-2222-2-2-2200000000-200002000000000000
χ3722-22-12-2-12-1-122-1-21-10012-1-1-2−i3i3−i3i32-2-2-1-1-1-1110−i3i30−i3i300100001−i3i3−i3i300000000
χ3822-22-12-2-12-1-122-1-21-10012-1-1-2i3−i3i3−i32-2-2-1-1-1-1110i3−i30i3−i300100001i3−i3i3−i300000000
χ3922-22-12-2-12-1-1-2-2-1-21-10012-1-1-2−i3i3−i3i3-2221111110−i3i30−i3i300-10000-1i3−i3i3−i300000000
χ4022-22-12-2-12-1-1-2-2-1-21-10012-1-1-2i3−i3i3−i3-2221111110i3−i30i3−i300-10000-1−i3i3−i3i300000000
χ4122-22-1-22-121122-1-21-100-1-21123−3−33-22-211-1-11-103−30−3300-1000013−3−3300000000
χ4222-22-1-22-121122-1-21-100-1-2112−333−3-22-211-1-11-10−3303−300-100001−333−300000000
χ4322-22-1-22-1211-2-2-1-21-100-1-21123−3−332-22-1-1111-103−30−330010000-1−333−300000000
χ4422-22-1-22-1211-2-2-1-21-100-1-2112−333−32-22-1-1111-10−3303−30010000-13−3−3300000000
χ45444-2-244-2-2-2-2001-2-2144-2-211-2-2-2-2-2000000011-211-21100000000000000000000
χ46444-2-244-2-2-2-2001-2-21-4-4-2-211-222220000000112-1-12-1-100000000000000000000
χ47444-2-2-4-4-2-222001-2-214i−4i22-1-12−2i−2i2i2i00000001-1−2iii2i−i−i00000000000000000000
χ48444-2-2-4-4-2-222001-2-21−4i4i22-1-122i2i−2i−2i00000001-12i−i−i−2iii00000000000000000000
χ4944-4-244-44-24400-22-4-200-4-2-2-22000000000002200000000000000000000000000
χ5044-4-24-444-2-4-400-22-4-2004222-2000000000002-200000000000000000000000000
χ5144-4-2-24-4-2-2-2-2001221002-2112−2i32i3−2i32i30000000-1-10i3−i30i3−i300000000000000000000
χ5244-4-2-24-4-2-2-2-2001221002-21122i3−2i32i3−2i30000000-1-10−i3i30−i3i300000000000000000000
χ5344-4-2-2-44-2-22200122100-22-1-1-223−23−23230000000-110−3303−300000000000000000000
χ5444-4-2-2-44-2-22200122100-22-1-1-2−232323−230000000-1103−30−3300000000000000000000
χ554-404400-4-4004i−4i400-400000000000000004i−4i0000000000000000000000000000
χ564-404400-4-400−4i4i400-40000000000000000−4i4i0000000000000000000000000000
χ574-404-2002-423−234i−4i-2002000023−2300000000−2i32i3−2i2i0000000000000000000000000000
χ584-404-2002-423−23−4i4i-2002000023−23000000002i3−2i32i−2i0000000000000000000000000000
χ594-404-2002-4−23234i−4i-20020000−2323000000002i3−2i3−2i2i0000000000000000000000000000
χ604-404-2002-4−2323−4i4i-20020000−232300000000−2i32i32i−2i0000000000000000000000000000
χ618-80-4800-840000-40040000000000000000000000000000000000000000000000
χ628-80-4-4004443−4300200-20000−23230000000000000000000000000000000000000000
χ638-80-4-40044−434300200-2000023−230000000000000000000000000000000000000000

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