Finite Group Databasebeta

← Group #72342969

Character table — Group #72342969

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112226666661212121212121232323232323232324848484848484848112226666661212121212121232323232323232324848484848484848
order12488222444248888836121224242424244444442248822244424888886612122424242424444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111-1-111111111-1-1-1-1-11111-1-1-1-11-1111-1-1-1111-1-111111111-1-1-1-1-11111-1-1-1-11-1111-1-1-1
χ4111-1-111111111-1-1-1-1-11111-1-1-1-1-11-1-1-1111111-1-111111111-1-1-1-1-11111-1-1-1-1-11-1-1-1111
χ5222222222222222222-1-1-1-1-1-1-1-100000000222222222222222222-1-1-1-1-1-1-1-100000000
χ6222-2-222222222-2-2-2-2-2-1-1-1-1111100000000222-2-222222222-2-2-2-2-2-1-1-1-1111100000000
χ722-200222-2-2-2-220000022-2-200000000000022-200222-2-2-2-220000022-2-2000000000000
χ822-200222-2-2-2-2200000-1-11133−3−30000000022-200222-2-2-2-2200000-1-11133−3−300000000
χ922-200222-2-2-2-2200000-1-111−3−3330000000022-200222-2-2-2-2200000-1-111−3−33300000000
χ10333333-1-13-1-1-1-13-1-1-1-100000000111-1-11-1-1333333-1-13-1-1-1-13-1-1-1-100000000111-1-11-1-1
χ11333333-1-13-1-1-1-13-1-1-1-100000000-1-1-111-111333333-1-13-1-1-1-13-1-1-1-100000000-1-1-111-111
χ1233333-13-1-13-1-1-1-13-1-1-10000000011-11-1-11-133333-13-1-13-1-1-1-13-1-1-10000000011-11-1-11-1
χ1333333-13-1-13-1-1-1-13-1-1-100000000-1-11-111-1133333-13-1-13-1-1-1-13-1-1-100000000-1-11-111-11
χ1433333-1-13-1-13-1-1-1-13-1-10000000011-1-11-1-1133333-1-13-1-13-1-1-1-13-1-10000000011-1-11-1-11
χ1533333-1-13-1-13-1-1-1-13-1-100000000-1-111-111-133333-1-13-1-13-1-1-1-13-1-100000000-1-111-111-1
χ16333-3-33-1-13-1-1-1-1-31111000000001-11-1-1-111333-3-33-1-13-1-1-1-1-31111000000001-11-1-1-111
χ17333-3-33-1-13-1-1-1-1-3111100000000-11-1111-1-1333-3-33-1-13-1-1-1-1-3111100000000-11-1111-1-1
χ18333-3-3-13-1-13-1-1-11-3111000000001-1-11-11-11333-3-3-13-1-13-1-1-11-3111000000001-1-11-11-11
χ19333-3-3-13-1-13-1-1-11-311100000000-111-11-11-1333-3-3-13-1-13-1-1-11-311100000000-111-11-11-1
χ20333-3-3-1-13-1-13-1-111-311000000001-1-1-1111-1333-3-3-1-13-1-13-1-111-311000000001-1-1-1111-1
χ21333-3-3-1-13-1-13-1-111-31100000000-1111-1-1-11333-3-3-1-13-1-13-1-111-31100000000-1111-1-1-11
χ2266666-2-2-2-2-2-222-2-2-222000000000000000066666-2-2-2-2-2-222-2-2-2220000000000000000
χ23666-6-6-2-2-2-2-2-222222-2-20000000000000000666-6-6-2-2-2-2-2-222222-2-20000000000000000
χ2466-6006-2-2-6222-200000000000000000000066-6006-2-2-6222-2000000000000000000000
χ2566-600-26-22-622-200000000000000000000066-600-26-22-622-2000000000000000000000
χ2666-600-2-2622-62-200000000000000000000066-600-2-2622-62-2000000000000000000000
χ2766-600-2-2-2222-220004i−4i000000000000000066-600-2-2-2222-220004i−4i0000000000000000
χ2866-600-2-2-2222-22000−4i4i000000000000000066-600-2-2-2222-22000−4i4i0000000000000000
χ298-80−4i24i200000000000002-200−i2i2−i2i2000000008-80−4i24i200000000000002-200−i2i2−i2i200000000
χ308-80−4i24i20000000000000-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000008-80−4i24i20000000000000-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ318-80−4i24i20000000000000-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000008-80−4i24i20000000000000-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ328-804i2−4i200000000000002-200i2−i2i2−i2000000008-804i2−4i200000000000002-200i2−i2i2−i200000000
χ338-804i2−4i20000000000000-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000008-804i2−4i20000000000000-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ348-804i2−4i20000000000000-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000008-804i2−4i20000000000000-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ37111-1-111111111-1-1-1-1-11111-1-1-1-11-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-11111-11-1-1-1111
χ38111-1-111111111-1-1-1-1-11111-1-1-1-1-11-1-1-1111-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111111-1111-1-1-1
χ39222222222222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111100000000
χ40222-2-222222222-2-2-2-2-2-1-1-1-1111100000000-2-2-222-2-2-2-2-2-2-2-2222221111-1-1-1-100000000
χ4122-200222-2-2-2-220000022-2-2000000000000-2-2200-2-2-22222-200000-2-222000000000000
χ4222-200222-2-2-2-2200000-1-11133−3−300000000-2-2200-2-2-22222-20000011-1-1−3−33300000000
χ4322-200222-2-2-2-2200000-1-111−3−33300000000-2-2200-2-2-22222-20000011-1-133−3−300000000
χ44333333-1-13-1-1-1-13-1-1-1-100000000111-1-11-1-1-3-3-3-3-3-311-31111-3111100000000-1-1-111-111
χ45333333-1-13-1-1-1-13-1-1-1-100000000-1-1-111-111-3-3-3-3-3-311-31111-3111100000000111-1-11-1-1
χ4633333-13-1-13-1-1-1-13-1-1-10000000011-11-1-11-1-3-3-3-3-31-311-31111-311100000000-1-11-111-11
χ4733333-13-1-13-1-1-1-13-1-1-100000000-1-11-111-11-3-3-3-3-31-311-31111-31110000000011-11-1-11-1
χ4833333-1-13-1-13-1-1-1-13-1-10000000011-1-11-1-11-3-3-3-3-311-311-31111-31100000000-1-111-111-1
χ4933333-1-13-1-13-1-1-1-13-1-100000000-1-111-111-1-3-3-3-3-311-311-31111-3110000000011-1-11-1-11
χ50333-3-33-1-13-1-1-1-1-31111000000001-11-1-1-111-3-3-333-311-311113-1-1-1-100000000-11-1111-1-1
χ51333-3-33-1-13-1-1-1-1-3111100000000-11-1111-1-1-3-3-333-311-311113-1-1-1-1000000001-11-1-1-111
χ52333-3-3-13-1-13-1-1-11-3111000000001-1-11-11-11-3-3-3331-311-3111-13-1-1-100000000-111-11-11-1
χ53333-3-3-13-1-13-1-1-11-311100000000-111-11-11-1-3-3-3331-311-3111-13-1-1-1000000001-1-11-11-11
χ54333-3-3-1-13-1-13-1-111-311000000001-1-1-1111-1-3-3-33311-311-311-1-13-1-100000000-1111-1-1-11
χ55333-3-3-1-13-1-13-1-111-31100000000-1111-1-1-11-3-3-33311-311-311-1-13-1-1000000001-1-1-1111-1
χ5666666-2-2-2-2-2-222-2-2-2220000000000000000-6-6-6-6-6222222-2-2222-2-20000000000000000
χ57666-6-6-2-2-2-2-2-222222-2-20000000000000000-6-6-666222222-2-2-2-2-2220000000000000000
χ5866-6006-2-2-6222-2000000000000000000000-6-6600-6226-2-2-22000000000000000000000
χ5966-600-26-22-622-2000000000000000000000-6-66002-62-26-2-22000000000000000000000
χ6066-600-2-2622-62-2000000000000000000000-6-660022-6-2-26-22000000000000000000000
χ6166-600-2-2-2222-220004i−4i0000000000000000-6-6600222-2-2-22-2000−4i4i0000000000000000
χ6266-600-2-2-2222-22000−4i4i0000000000000000-6-6600222-2-2-22-20004i−4i0000000000000000
χ638-80−4i24i200000000000002-200−i2i2−i2i200000000-8804i2−4i20000000000000-2200i2−i2i2−i200000000
χ648-80−4i24i20000000000000-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000-8804i2−4i200000000000001-1−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ658-80−4i24i20000000000000-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000-8804i2−4i200000000000001-13−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ668-804i2−4i200000000000002-200i2−i2i2−i200000000-880−4i24i20000000000000-2200−i2i2−i2i200000000
χ678-804i2−4i20000000000000-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000-880−4i24i200000000000001-1−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ688-804i2−4i20000000000000-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000-880−4i24i200000000000001-13−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000

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