Finite Group Databasebeta

← Group #72343899

Character table — Group #72343899

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111116666888812121212121212122424242424242424323232323232323232323232323232324848484848484848484848484848
order1222444422442244222244448888888836666666121212121212121244444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1111111111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ4111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ51111-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-11-1ii−i−ii−ii−iii−i−i
χ61111-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-11-1−i−iii−ii−ii−i−iii
χ71111-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−i−i−iii111-1-1-1-11-1-1-1-11111-11−i−iii−iii−iii−i−i
χ81111-1-1-1-111-1-1-1-11111-1-111-1-1−i−iiiii−i−i111-1-1-1-11-1-1-1-11111-11ii−i−ii−i−ii−i−iii
χ922222222222222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000
χ10222222222222-2-2-2-22222222200000000-1-1-11111-1-1-1-1-11111-2-2000000000000
χ112222-2-2-2-222-2-222-2-222-2-222-2-200000000-1-1-1-1-1-1-1-1111111112-2000000000000
χ122222-2-2-2-222-2-2-2-22222-2-222-2-200000000-1-1-11111-11111-1-1-1-1-22000000000000
χ132-2-2222-2-2-222-200002-22-22-2-22000000002-2-20000222-2-2000000000000000000
χ142-2-2222-2-2-222-200002-22-22-2-2200000000-111−i3−i3i3i3-1-1-111−i3−i3i3i300000000000000
χ152-2-2222-2-2-222-200002-22-22-2-2200000000-111i3i3−i3−i3-1-1-111i3i3−i3−i300000000000000
χ162-2-22-2-222-22-2200002-2-222-22-2000000002-2-200002-2-222000000000000000000
χ172-2-22-2-222-22-2200002-2-222-22-200000000-111−i3−i3i3i3-111-1-1i3i3−i3−i300000000000000
χ182-2-22-2-222-22-2200002-2-222-22-200000000-111i3i3−i3−i3-111-1-1−i3−i3i3i300000000000000
χ193333333333333333-1-1-1-1-1-1-1-1111111110000000000000000-1-1-1-1-1-11111-1-1-1-1
χ203333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-11111-1-1-1-11111
χ21333333333333-3-3-3-3-1-1-1-1-1-1-1-11111-1-1-1-10000000000000000111111-1-111-1-1-1-1
χ22333333333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000011-1-1-1-111-1-11111
χ233333-3-3-3-333-3-333-3-3-1-111-1-111ii−i−iii−i−i0000000000000000-11−i−iiii−ii−i−i−iii
χ243333-3-3-3-333-3-333-3-3-1-111-1-111−i−iii−i−iii0000000000000000-11ii−i−i−ii−iiii−i−i
χ253333-3-3-3-333-3-3-3-333-1-111-1-111ii−i−i−i−iii00000000000000001-1ii−i−i−iii−i−i−iii
χ263333-3-3-3-333-3-3-3-333-1-111-1-111−i−iiiii−i−i00000000000000001-1−i−iiii−i−iiii−i−i
χ2744-4-44i−4i4i−4i00002-22i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1311-11-11-1-1i−ii−ii−ii−i00000000000000
χ2844-4-44i−4i4i−4i00002-22i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1311-11-11-1-1i−ii−ii−ii−i00000000000000
χ2944-4-44i−4i4i−4i0000-22−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1311-1-11-11-1i−ii−i−ii−ii00000000000000
χ3044-4-44i−4i4i−4i0000-22−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1311-1-11-11-1i−ii−i−ii−ii00000000000000
χ3144-4-4−4i4i−4i4i00002-2−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2311-11-11-1-1−ii−ii−ii−ii00000000000000
χ3244-4-4−4i4i−4i4i00002-2−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2311-11-11-1-1−ii−ii−ii−ii00000000000000
χ3344-4-4−4i4i−4i4i0000-222i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2311-1-11-11-1−ii−iii−ii−i00000000000000
χ3444-4-4−4i4i−4i4i0000-222i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2311-1-11-11-1−ii−iii−ii−i00000000000000
χ3566666666-2-2-2-2000022-2-2-2-22222220000000000000000000000000000-2-20000
χ3666666666-2-2-2-2000022-2-2-2-222-2-2-2-20000000000000000000000000000220000
χ3766666666-2-2-2-20000-2-22222-2-2000022220000000000000000000000-2-2000000
χ3866666666-2-2-2-20000-2-22222-2-20000-2-2-2-2000000000000000000000022000000
χ396666-6-6-6-6-2-22200002222-2-2-2-22i2i−2i−2i0000000000000000000000000000−2i2i0000
χ406666-6-6-6-6-2-22200002222-2-2-2-2−2i−2i2i2i00000000000000000000000000002i−2i0000
χ416666-6-6-6-6-2-2220000-2-2-2-2222200002i2i−2i−2i0000000000000000000000−2i2i000000
χ426666-6-6-6-6-2-2220000-2-2-2-222220000−2i−2i2i2i00000000000000000000002i−2i000000
χ436-6-6666-6-62-2-2200002-2-22-22-2200000000000000000000000000000000002-22-2
χ446-6-6666-6-62-2-2200002-2-22-22-220000000000000000000000000000000000-22-22
χ456-6-6666-6-62-2-220000-222-22-22-2000000000000000000000000002i−2i2i−2i00000000
χ466-6-6666-6-62-2-220000-222-22-22-200000000000000000000000000−2i2i−2i2i00000000
χ476-6-6666-6-6-666-60000-22-22-222-200000000000000000000000000000000000000
χ486-6-66-6-6662-22-200002-22-2-222-200000000000000000000000000000000002i−2i−2i2i
χ496-6-66-6-6662-22-200002-22-2-222-20000000000000000000000000000000000−2i2i2i−2i
χ506-6-66-6-6662-22-20000-22-222-2-22000000000000000000000000002-2-2200000000
χ516-6-66-6-6662-22-20000-22-222-2-2200000000000000000000000000-222-200000000
χ526-6-66-6-666-66-660000-222-2-22-2200000000000000000000000000000000000000
χ5388-8-88i−8i8i−8i00004-44i−4i0000000000000000-1-11-11-111−ii−ii−ii−ii00000000000000
χ5488-8-88i−8i8i−8i0000-44−4i4i0000000000000000-1-111-11-11−ii−iii−ii−i00000000000000
χ5588-8-8−8i8i−8i8i00004-4−4i4i0000000000000000-1-11-11-111i−ii−ii−ii−i00000000000000
χ5688-8-8−8i8i−8i8i0000-444i−4i0000000000000000-1-111-11-11i−ii−i−ii−ii00000000000000
χ578-88-88i−8i−8i8i0000000000000000000000002-220000-22i−2i−2i2i000000000000000000
χ588-88-88i−8i−8i8i000000000000000000000000-11-1−i3i3i3−i31−iii−i3−3−3300000000000000
χ598-88-88i−8i−8i8i000000000000000000000000-11-1i3−i3−i3i31−iii−i−333−300000000000000
χ608-88-8−8i8i8i−8i0000000000000000000000002-220000-2−2i2i2i−2i000000000000000000
χ618-88-8−8i8i8i−8i000000000000000000000000-11-1−i3i3i3−i31i−i−ii−333−300000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000-11-1i3−i3−i3i31i−i−ii3−3−3300000000000000

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