Finite Group Databasebeta

← Group #72242853

Character table — Group #72242853

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111333312121212121212121212121224242424242424244848484848484848484848484848128128128128
order1222222222222222444444444444444444444488883666
χ11111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311-1-1-111-11111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iii−i−i11-1-1
χ411-1-1-111-11111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−iii11-1-1
χ5222222222222222222220000000022000000000000-1-1-1-1
χ622-2-2-222-22222-2-2-2-222-2-2000000002-2000000000000-1-111
χ73333333333-1-13-13-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-10000
χ83333333333-1-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111110000
χ933333333-1-133-13-13-1-1-1-111111111-1-1-1-111-1-111-1-1-1-10000
χ1033333333-1-133-13-13-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111110000
χ1133333333-1-1-1-1-1-1-1-1333311111111-1-1-1-1-1-1-1-1-1-111110000
χ1233333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-111111111-1-1-1-10000
χ1333-3-3-333-333-1-1-31-31-1-111ii−i−iii−i−i-11ii−i−i−i−iii−i−iii0000
χ1433-3-3-333-333-1-1-31-31-1-111−i−iii−i−iii-11−i−iiiii−i−iii−i−i0000
χ1533-3-3-333-3-1-1331-31-3-1-111ii−i−iii−i−i-11−i−iiiii−i−i−i−iii0000
χ1633-3-3-333-3-1-1331-31-3-1-111−i−iii−i−iii-11ii−i−i−i−iiiii−i−i0000
χ1733-3-3-333-3-1-1-1-1111133-3-3ii−i−iii−i−i-11−i−i−i−iiiiiii−i−i0000
χ1833-3-3-333-3-1-1-1-1111133-3-3−i−iii−i−iii-11iiii−i−i−i−i−i−iii0000
χ194-44-444-4-40000000000002i−2i2i−2i2i−2i2i−2i000000000000001-11-1
χ204-44-444-4-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000001-11-1
χ214-4-44-44-440000000000002-2-222-2-22000000000000001-1-11
χ224-4-44-44-44000000000000-222-2-222-2000000000000001-1-11
χ2366666666-2-2-2-2-2-2-2-2-2-2-2-200000000220000000000000000
χ2466-6-6-666-6-2-2-2-22222-2-222000000002-20000000000000000
χ256-66-6-2-2222-22-222-2-22-2-222i−2i2i−2i−2i2i−2i2i000000000000000000
χ266-66-6-2-2222-22-222-2-22-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000
χ276-66-6-2-2222-2-222-2-22-222-200000000002i−2i002i−2i0000000000
χ286-66-6-2-2222-2-222-2-22-222-20000000000−2i2i00−2i2i0000000000
χ296-66-6-2-222-222-2-222-2-222-20000000000002i−2i002i−2i00000000
χ306-66-6-2-222-222-2-222-2-222-2000000000000−2i2i00−2i2i00000000
χ316-66-6-2-222-22-22-2-2222-2-220000000000000000002-22-20000
χ326-66-6-2-222-22-22-2-2222-2-22000000000000000000-22-220000
χ336-6-662-22-22-22-2-2-2222-22-22-2-22-222-2000000000000000000
χ346-6-662-22-22-22-2-2-2222-22-2-222-22-2-22000000000000000000
χ356-6-662-22-22-2-22-222-2-22-2200000000002-200-220000000000
χ366-6-662-22-22-2-22-222-2-22-220000000000-22002-20000000000
χ376-6-662-22-2-222-22-2-22-22-220000000000002-200-2200000000
χ386-6-662-22-2-222-22-2-22-22-22000000000000-22002-200000000
χ396-6-662-22-2-22-2222-2-22-22-20000000000000000002i−2i−2i2i0000
χ406-6-662-22-2-22-2222-2-22-22-2000000000000000000−2i2i2i−2i0000
χ418-88-888-8-80000000000000000000000000000000000-11-11
χ428-8-88-88-880000000000000000000000000000000000-111-1
χ4312121212-4-4-4-40000000000002222-2-2-2-2000000000000000000
χ4412121212-4-4-4-4000000000000-2-2-2-22222000000000000000000
χ451212-12-124-4-440000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ461212-12-124-4-44000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000

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