Finite Group Databasebeta

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3−1+2×#5077 #72220020

order5184
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23

Aliases

direct product3−1+2×#5077

Splittings

FittingC3×3−1+2×#127 ⋊ C2
SylowC3×3−1+2 ⋊ #453

Subgroups

subgroupG/H
centerC2×C3C32×#937
commutator, cosocleC2×C32×C4C23×C32
FrattiniC2×C3×C4C22×C32×D3
FittingC3×3−1+2×#127C2
socleC2×C32C32×#120
prime radicalC32×#5077C3
hypercenter3−1+2×#127D3
hypocenterC33−1+2×#453
LCSG ▷ C2×C32×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C4×3−1+2 ◁ 3−1+2×#127

1938 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#72220022, #72220090
maximal normal subgroup of#72220090
maximal quotient of#72220022

GAP

Past the SmallGroups library coverage — no SmallGroups id.