Finite Group Databasebeta

← Group #72341893

Character table — Group #72341893

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222266666666666612121212121212121212121212123232323232323232323232323232323248484848484848484848484848484848
order12442444442222224444442244444444444436661212121212121212121212122444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511-1-1-11ii−i−i-1-1-1111111-1-1-11-11-1iiiii−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-1111-1-1-1i−iiii−i−i−i
χ611-1-1-11ii−i−i-1-1-1111111-1-1-11-11-1iiiii−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11-1-1-1111−ii−i−i−iiii
χ711-1-1-11−i−iii-1-1-1111111-1-1-11-11-1−i−i−i−i−iiiiii11-1-111-1-1−i−i−i−iiiii1-1111-1-1-1−ii−i−i−iiii
χ811-1-1-11−i−iii-1-1-1111111-1-1-11-11-1−i−i−i−i−iiiiii11-1-111-1-1−i−i−i−iiiii-11-1-1-1111i−iiii−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
χ112222-2-20000-2-2-2222-2-2-2222-222-2000000000022-2-2-2-222000000000000000000000000
χ122222-2-20000-2-2-2222-2-2-2222-222-20000000000-1-11111-1-133−3−333−3−30000000000000000
χ132222-2-20000-2-2-2222-2-2-2222-222-20000000000-1-11111-1-1−3−333−3−3330000000000000000
χ1422-2-22-20000222222-2-2-2-2-2-2-2-22200000000002222-2-2-2-2000000000000000000000000
χ1522-2-22-20000222222-2-2-2-2-2-2-2-2220000000000-1-1-1-11111−i3−i3i3i3i3i3−i3−i30000000000000000
χ1622-2-22-20000222222-2-2-2-2-2-2-2-2220000000000-1-1-1-11111i3i3−i3−i3−i3−i3i3i30000000000000000
χ1722-2-2-222i2i−2i−2i-2-2-2222222-2-2-22-22-22i2i2i2i2i−2i−2i−2i−2i−2i-1-111-1-111−i−i−i−iiiii0000000000000000
χ1822-2-2-22−2i−2i2i2i-2-2-2222222-2-2-22-22-2−2i−2i−2i−2i−2i2i2i2i2i2i-1-111-1-111iiii−i−i−i−i0000000000000000
χ1933333333333-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-10000000000000000111-1-11-1-1111-1-11-1-1
χ2033333333333-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1-10000000000000000-1-1-111-111-1-1-111-111
χ213333333333-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-1000000000000000011-11-1-11-111-11-1-11-1
χ223333333333-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1-10000000000000000-1-11-111-11-1-11-111-11
χ233333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-1000000000000000011-1-11-1-1111-1-11-1-11
χ243333333333-1-13-1-13-1-13-1-13-1-1-1-1-1-13-1-1-1-13-1-10000000000000000-1-111-111-1-1-111-111-1
χ25333333-3-3-3-33-1-13-1-13-1-13-1-1-1-1-1-1-31111-311110000000000000000111-1-11-1-1-1-1-111-111
χ26333333-3-3-3-33-1-13-1-13-1-13-1-1-1-1-1-1-31111-311110000000000000000-1-1-111-111111-1-11-1-1
χ27333333-3-3-3-3-13-1-13-1-13-1-13-1-1-1-1-11-31111-3111000000000000000011-11-1-11-1-1-11-111-11
χ28333333-3-3-3-3-13-1-13-1-13-1-13-1-1-1-1-11-31111-31110000000000000000-1-11-111-1111-11-1-11-1
χ29333333-3-3-3-3-1-13-1-13-1-13-1-13-1-1-1-111-31111-311000000000000000011-1-11-1-11-1-111-111-1
χ30333333-3-3-3-3-1-13-1-13-1-13-1-13-1-1-1-111-31111-3110000000000000000-1-111-111-111-1-11-1-11
χ3133-3-3-333i3i−3i−3i11-3-1-13-1-1311-3-11-11−i−i3i−i−iii−3iii00000000000000001-1-1-1111-1i−i−i−iiii−i
χ3233-3-3-333i3i−3i−3i11-3-1-13-1-1311-3-11-11−i−i3i−i−iii−3iii0000000000000000-1111-1-1-11−iiii−i−i−ii
χ3333-3-3-333i3i−3i−3i1-31-13-1-13-11-31-11-11−i3i−i−i−ii−3iiii00000000000000001-1-11-11-11i−i−ii−ii−ii
χ3433-3-3-333i3i−3i−3i1-31-13-1-13-11-31-11-11−i3i−i−i−ii−3iiii0000000000000000-111-11-11-1−iii−ii−ii−i
χ3533-3-3-333i3i−3i−3i-3113-1-13-1-1-311-11-113i−i−i−i−i−3iiiii00000000000000001-11-1-1-111i−ii−i−i−iii
χ3633-3-3-333i3i−3i−3i-3113-1-13-1-1-311-11-113i−i−i−i−i−3iiiii0000000000000000-11-1111-1-1−ii−iiii−i−i
χ3733-3-3-33−3i−3i3i3i11-3-1-13-1-1311-3-11-11ii−3iii−i−i3i−i−i00000000000000001-1-1-1111-1−iiii−i−i−ii
χ3833-3-3-33−3i−3i3i3i11-3-1-13-1-1311-3-11-11ii−3iii−i−i3i−i−i0000000000000000-1111-1-1-11i−i−i−iiii−i
χ3933-3-3-33−3i−3i3i3i1-31-13-1-13-11-31-11-11i−3iiii−i3i−i−i−i00000000000000001-1-11-11-11−iii−ii−ii−i
χ4033-3-3-33−3i−3i3i3i1-31-13-1-13-11-31-11-11i−3iiii−i3i−i−i−i0000000000000000-111-11-11-1i−i−ii−ii−ii
χ4133-3-3-33−3i−3i3i3i-3113-1-13-1-1-311-11-11−3iiiii3i−i−i−i−i00000000000000001-11-1-1-111−ii−iiii−i−i
χ4233-3-3-33−3i−3i3i3i-3113-1-13-1-1-311-11-11−3iiiii3i−i−i−i−i0000000000000000-11-1111-1-1i−ii−i−i−iii
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
χ456666-6-60000222-2-2-2222-2-2-2-222-20004i−4i0004i−4i00000000000000000000000000000000
χ466666-6-60000222-2-2-2222-2-2-2-222-2000−4i4i000−4i4i00000000000000000000000000000000
χ476666-6-6000022-6-2-2622-6-2-262-2-22000000000000000000000000000000000000000000
χ486666-6-600002-62-26-22-62-26-22-2-22000000000000000000000000000000000000000000
χ496666-6-60000-6226-2-2-6226-2-22-2-22000000000000000000000000000000000000000000
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
χ5366-6-66-60000-2-2-2-2-2-2222222-2-2220004-4000-4400000000000000000000000000000000
χ5466-6-66-60000-2-2-2-2-2-2222222-2-222000-440004-400000000000000000000000000000000
χ5566-6-6-666i6i−6i−6i222-2-2-2-2-2-22222-22-2−2i−2i−2i2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ5666-6-6-66−6i−6i6i6i222-2-2-2-2-2-22222-22-22i2i2i−2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ578-88i−8i004+4i−4−4i4−4i−4+4i000000000000000000000000002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ588-88i−8i004+4i−4−4i4−4i−4+4i00000000000000000000000000-11−i3i33−3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70000000000000000
χ598-88i−8i004+4i−4−4i4−4i−4+4i00000000000000000000000000-11i3−i3−33−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ110000000000000000
χ608-88i−8i00−4−4i4+4i−4+4i4−4i000000000000000000000000002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ618-88i−8i00−4−4i4+4i−4+4i4−4i00000000000000000000000000-11−i3i33−3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70000000000000000
χ628-88i−8i00−4−4i4+4i−4+4i4−4i00000000000000000000000000-11i3−i3−33−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ110000000000000000
χ638-8−8i8i004−4i−4+4i4+4i−4−4i000000000000000000000000002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ648-8−8i8i004−4i−4+4i4+4i−4−4i00000000000000000000000000-11−i3i3−33i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ70000000000000000
χ658-8−8i8i004−4i−4+4i4+4i−4−4i00000000000000000000000000-11i3−i33−3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110000000000000000
χ668-8−8i8i00−4+4i4−4i−4−4i4+4i000000000000000000000000002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ678-8−8i8i00−4+4i4−4i−4−4i4+4i00000000000000000000000000-11−i3i3−33i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ70000000000000000
χ688-8−8i8i00−4+4i4−4i−4−4i4+4i00000000000000000000000000-11i3−i33−3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.