Finite Group Databasebeta

← Group #10712003

Character table — Group #10712003

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222224444444444448888888888881212121212121212161616161616161616161616161624242424242424244848
order1244234612122224444444612246661212121212121288888888444461212121212121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ61111111111111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111
χ71111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-111-1-1
χ911-1-111-11-1-111-11-1-111-1-11-11-1-1111-1-111-1-1ii−i−iii−i−i1-11-11-111-1-111-1-1ii−i−ii−ii−ii−i
χ1011-1-111-11-1-111-11-1-111-1-11-11-1-1111-1-111-1-1ii−i−iii−i−i-11-111-1-1-111-1-111−i−iiii−ii−i−ii
χ1111-1-111-11-1-111-11-1-111-1-11-11-1-1111-1-111-1-1−i−iii−i−iii1-11-11-111-1-111-1-1−i−iii−ii−ii−ii
χ1211-1-111-11-1-111-11-1-111-1-11-11-1-1111-1-111-1-1−i−iii−i−iii-11-111-1-1-111-1-111ii−i−i−ii−iii−i
χ1311-1-111-11-1-111-11-1-1-1-1111-1-11-1111-1-1-1-111ii−i−i−i−iii1-1-11-1111-1-1-1-111ii−i−ii−i−ii−ii
χ1411-1-111-11-1-111-11-1-1-1-1111-1-11-1111-1-1-1-111ii−i−i−i−iii-111-1-11-1-11111-1-1−i−iiii−i−iii−i
χ1511-1-111-11-1-111-11-1-1-1-1111-1-11-1111-1-1-1-111−i−iiiii−i−i1-1-11-1111-1-1-1-111−i−iii−iii−ii−i
χ1611-1-111-11-1-111-11-1-1-1-1111-1-11-1111-1-1-1-111−i−iiiii−i−i-111-1-11-1-11111-1-1ii−i−i−iii−i−ii
χ1722222222222-2-2-22-200002200-22-2-22-200000000222200000000000000000000-2-200
χ1822222222222-2-2-22-200002200-22-2-22-200000000-2-2-2-2000000000000000000002200
χ192222222222-22-2-2-2200002200-2-22-2-22000022220000000000000000000000-2-20000
χ202222222222-22-2-2-2200002200-2-22-2-220000-2-2-2-20000000000000000000000220000
χ212222222222-2-222-2-2222222-2-22-2-22-2-22222000000000000-2-2000000000000000000
χ222222222222-2-222-2-2-2-2-2-222222-2-22-2-2-2-2-2-200000000000022000000000000000000
χ2322222-12-1-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-10000000000
χ2422222-12-1-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111110000000000
χ2522222-12-1-1-1222222-2-2-2-2-1-1-2-2-1-1-1-1-1-111110000000022-2-211-1-1-1-111110000000000
χ2622222-12-1-1-1222222-2-2-2-2-1-1-2-2-1-1-1-1-1-1111100000000-2-222111111-1-1-1-10000000000
χ2722222-12-1-1-1-2-222-2-22222-1-1-2-2-111-111-1-1-1-1000000000000113−33−33−33−30000000000
χ2822222-12-1-1-1-2-222-2-22222-1-1-2-2-111-111-1-1-1-100000000000011−33−33−33−330000000000
χ2922222-12-1-1-1-2-222-2-2-2-2-2-2-1-122-111-1111111000000000000-1-13−33−3−33−330000000000
χ3022222-12-1-1-1-2-222-2-2-2-2-2-2-1-122-111-1111111000000000000-1-1−33−333−33−30000000000
χ3122-2-222-22-2-22-22-2-2200002-20022-2-2-22000000002i2i−2i−2i00000000000000000000−2i2i00
χ3222-2-222-22-2-22-22-2-2200002-20022-2-2-2200000000−2i−2i2i2i000000000000000000002i−2i00
χ3322-2-222-22-2-2-222-22-200002-2002-22-22-200002i2i−2i−2i0000000000000000000000−2i2i0000
χ3422-2-222-22-2-2-222-22-200002-2002-22-22-20000−2i−2i2i2i00000000000000000000002i−2i0000
χ3522-2-222-22-2-2-2-2-222222-2-22-2-22-2-2-222222-2-2000000000000-22000000000000000000
χ3622-2-222-22-2-2-2-2-2222-2-2222-22-2-2-2-2222-2-2220000000000002-2000000000000000000
χ3722-2-22-1-2-11122-22-2-222-2-2-112-21-1-1-111-1-111000000002-22-2-11-1-111-1-1110000000000
χ3822-2-22-1-2-11122-22-2-222-2-2-112-21-1-1-111-1-11100000000-22-22-1111-1-111-1-10000000000
χ3922-2-22-1-2-11122-22-2-2-2-222-11-221-1-1-11111-1-1000000002-2-221-1-1-11111-1-10000000000
χ4022-2-22-1-2-11122-22-2-2-2-222-11-221-1-1-11111-1-100000000-222-21-111-1-1-1-1110000000000
χ4122-2-22-1-2-111-2-2-222222-2-2-11-22111-1-1-1-1-1110000000000001-13−3−333−3−330000000000
χ4222-2-22-1-2-111-2-2-222222-2-2-11-22111-1-1-1-1-1110000000000001-1−333−3−333−30000000000
χ4322-2-22-1-2-111-2-2-2222-2-222-112-2111-1-1-111-1-1000000000000-113−3−33−333−30000000000
χ4422-2-22-1-2-111-2-2-2222-2-222-112-2111-1-1-111-1-1000000000000-11−333−33−3−330000000000
χ4544444-24-2-2-24-4-4-44-40000-2-2002-222-22000000000000000000000000000000000000
χ4644444-24-2-2-2-44-4-4-440000-2-20022-222-2000000000000000000000000000000000000
χ474444-44-44440000000000-4-400000000000000000000000000000000002-22-2000000
χ484444-44-44440000000000-4-40000000000000000000000000000000000-22-22000000
χ4944-4-44-2-4-2224-44-4-440000-2200-2-2222-2000000000000000000000000000000000000
χ5044-4-44-2-4-222-444-44-40000-2200-22-22-22000000000000000000000000000000000000
χ5144-4-4-4444-4-40000000000-4400000000000000000000000000000000002i−2i−2i2i000000
χ5244-4-4-4444-4-40000000000-440000000000000000000000000000000000−2i2i2i−2i000000
χ534-44i−4i040-44i−4i0000002-22i−2i00000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ544-44i−4i040-44i−4i0000002-22i−2i00000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ554-44i−4i040-44i−4i000000-22−2i2i0000000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ564-44i−4i040-44i−4i000000-22−2i2i0000000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ574-4−4i4i040-4−4i4i0000002-2−2i2i00000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ584-4−4i4i040-4−4i4i0000002-2−2i2i00000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ594-4−4i4i040-4−4i4i000000-222i−2i0000000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ604-4−4i4i040-4−4i4i000000-222i−2i0000000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ618888-8-4-8-4-4-400000000004400000000000000000000000000000000000000000000
χ6288-8-8-8-48-44400000000004-400000000000000000000000000000000000000000000
χ638-88i−8i0-404−4i4i0000004-44i−4i0000000000-22−2i2i00000000000000000000000000000000
χ648-88i−8i0-404−4i4i000000-44−4i4i00000000002-22i−2i00000000000000000000000000000000
χ658-8−8i8i0-4044i−4i0000004-4−4i4i0000000000-222i−2i00000000000000000000000000000000
χ668-8−8i8i0-4044i−4i000000-444i−4i00000000002-2−2i2i00000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.