Finite Group Databasebeta

← Group #72341672

Character table — Group #72341672

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222266666666666612121212121212121212121212123232323232323232323232323232323248484848484848484848484848484848
order12442488882222224444442244888888888836661212121224242424242424248888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511-1-1-1111-1-1111-1-1-1111-1-1-11-11-111111-1-1-1-1-11-1-11-1-1111111-1-1-1-1i−ii−iiii−i−i−iiii−i−i−i
χ611-1-1-1111-1-1111-1-1-1111-1-1-11-11-111111-1-1-1-1-11-1-11-1-1111111-1-1-1-1−ii−ii−i−i−iiii−i−i−iiii
χ711-1-1-11-1-111111-1-1-1111-1-1-11-11-1-1-1-1-1-1111111-1-11-1-111-1-1-1-11111i−i−iiiii−i−i−i−i−i−iiii
χ811-1-1-11-1-111111-1-1-1111-1-1-11-11-1-1-1-1-1-1111111-1-11-1-111-1-1-1-11111−iii−i−i−i−iiiiiii−i−i−i
χ9222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ10222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ112222-2-20000222-2-2-2-2-2-2222-222-200000000002-2-2222-2-2000000000000000000000000
χ122222-2-20000222-2-2-2-2-2-2222-222-20000000000-111-1-1-11133−3−333−3−30000000000000000
χ132222-2-20000222-2-2-2-2-2-2222-222-20000000000-111-1-1-111−3−333−3−3330000000000000000
χ1422-2-22-20000222222-2-2-2-2-2-2-2-22200000000002222-2-2-2-2000000000000000000000000
χ1522-2-22-20000222222-2-2-2-2-2-2-2-2220000000000-1-1-1-1111133−3−3−3−3330000000000000000
χ1622-2-22-20000222222-2-2-2-2-2-2-2-2220000000000-1-1-1-11111−3−33333−3−30000000000000000
χ1722-2-2-2222-2-2222-2-2-2222-2-2-22-22-222222-2-2-2-2-2-111-111-1-1-1-1-1-111110000000000000000
χ1822-2-2-22-2-222222-2-2-2222-2-2-22-22-2-2-2-2-2-222222-111-111-1-11111-1-1-1-10000000000000000
χ1933333333333-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-1000000000000000011111-1-11-1-11-1-11-1-1
χ2033333333333-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-10000000000000000-1-1-1-1-111-111-111-111
χ213333333333-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-100000000000000001111-11-1-11-1-11-1-11-1
χ223333333333-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-10000000000000000-1-1-1-11-111-111-111-11
χ233333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-100000000000000001111-1-11-1-11-1-11-1-11
χ243333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-10000000000000000-1-1-1-111-111-111-111-1
χ25333333-3-3-3-33-1-13-1-13-1-13-1-1-1-1-1-1-31111-31111000000000000000011-1-11-1-11-1-1-111-111
χ26333333-3-3-3-33-1-13-1-13-1-13-1-1-1-1-1-1-31111-311110000000000000000-1-111-111-1111-1-11-1-1
χ27333333-3-3-3-3-13-1-13-1-13-1-13-1-1-1-1-11-31111-3111000000000000000011-1-1-11-1-11-11-111-11
χ28333333-3-3-3-3-13-1-13-1-13-1-13-1-1-1-1-11-31111-31110000000000000000-1-1111-111-11-11-1-11-1
χ29333333-3-3-3-3-1-13-1-13-1-13-1-13-1-1-1-111-31111-311000000000000000011-1-1-1-11-1-1111-111-1
χ30333333-3-3-3-3-1-13-1-13-1-13-1-13-1-1-1-111-31111-3110000000000000000-1-11111-111-1-1-11-1-11
χ3133-3-3-3333-3-33-1-1-3113-1-1-311-11-113-1-1-1-1-311110000000000000000i−ii−ii−i−i−iiii−i−i−iii
χ3233-3-3-3333-3-33-1-1-3113-1-1-311-11-113-1-1-1-1-311110000000000000000−ii−ii−iiii−i−i−iiii−i−i
χ3333-3-3-3333-3-3-13-11-31-13-11-31-11-11-13-1-1-11-31110000000000000000i−ii−i−ii−ii−ii−ii−ii−ii
χ3433-3-3-3333-3-3-13-11-31-13-11-31-11-11-13-1-1-11-31110000000000000000−ii−iii−ii−ii−ii−ii−ii−i
χ3533-3-3-3333-3-3-1-1311-3-1-1311-3-11-11-1-13-1-111-3110000000000000000i−ii−i−i−iiii−i−i−iiii−i
χ3633-3-3-3333-3-3-1-1311-3-1-1311-3-11-11-1-13-1-111-3110000000000000000−ii−iiii−i−i−iiii−i−i−ii
χ3733-3-3-33-3-3333-1-1-3113-1-1-311-11-11-311113-1-1-1-10000000000000000i−i−iii−i−i−iii−iiii−i−i
χ3833-3-3-33-3-3333-1-1-3113-1-1-311-11-11-311113-1-1-1-10000000000000000−iii−i−iiii−i−ii−i−i−iii
χ3933-3-3-33-3-333-13-11-31-13-11-31-11-111-3111-13-1-1-10000000000000000i−i−ii−ii−ii−iii−ii−ii−i
χ4033-3-3-33-3-333-13-11-31-13-11-31-11-111-3111-13-1-1-10000000000000000−iii−ii−ii−ii−i−ii−ii−ii
χ4133-3-3-33-3-333-1-1311-3-1-1311-3-11-1111-311-1-13-1-10000000000000000i−i−ii−i−iiii−iii−i−i−ii
χ4233-3-3-33-3-333-1-1311-3-1-1311-3-11-1111-311-1-13-1-10000000000000000−iii−iii−i−i−ii−i−iiii−i
χ436666666666-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-222-2-2-22200000000000000000000000000000000
χ44666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2222-2-200000000000000000000000000000000
χ456666-6-600006-2-2-622-6226-2-22-2-22000000000000000000000000000000000000000000
χ466666-6-60000-26-22-622-62-26-22-2-22000000000000000000000000000000000000000000
χ476666-6-60000-2-2622-622-6-2-262-2-22000000000000000000000000000000000000000000
χ486666-6-60000-2-2-2222222-2-2-2-222-20004i−4i0004i−4i00000000000000000000000000000000
χ496666-6-60000-2-2-2222222-2-2-2-222-2000−4i4i000−4i4i00000000000000000000000000000000
χ5066-6-66-600006-2-26-2-2-622-62222-2-2000000000000000000000000000000000000000000
χ5166-6-66-60000-26-2-26-22-622-6222-2-2000000000000000000000000000000000000000000
χ5266-6-66-60000-2-26-2-2622-622-622-2-2000000000000000000000000000000000000000000
χ5366-6-66-60000-2-2-2-2-2-2222222-2-2220004i−4i000−4i4i00000000000000000000000000000000
χ5466-6-66-60000-2-2-2-2-2-2222222-2-222000−4i4i0004i−4i00000000000000000000000000000000
χ5566-6-6-6666-6-6-2-2-2222-2-2-22222-22-2-2-2-222222-2-200000000000000000000000000000000
χ5666-6-6-66-6-666-2-2-2222-2-2-22222-22-2222-2-2-2-2-22200000000000000000000000000000000
χ578-88i−8i0042−42−4i24i200000000000000000000000000200-22i−2i002−22−2−i2i2−i2i20000000000000000
χ588-88i−8i0042−42−4i24i200000000000000000000000000-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ598-88i−8i0042−42−4i24i200000000000000000000000000-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ608-88i−8i00−42424i2−4i200000000000000000000000000200-22i−2i00−22−22i2−i2i2−i20000000000000000
χ618-88i−8i00−42424i2−4i200000000000000000000000000-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ628-88i−8i00−42424i2−4i200000000000000000000000000-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ638-8−8i8i0042−424i2−4i200000000000000000000000000200-2−2i2i002−22−2i2−i2i2−i20000000000000000
χ648-8−8i8i0042−424i2−4i200000000000000000000000000-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ658-8−8i8i0042−424i2−4i200000000000000000000000000-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ668-8−8i8i00−4242−4i24i200000000000000000000000000200-2−2i2i00−22−22−i2i2−i2i20000000000000000
χ678-8−8i8i00−4242−4i24i200000000000000000000000000-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ688-8−8i8i00−4242−4i24i200000000000000000000000000-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000

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