Finite Group Databasebeta

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C3×#16861375 #27133569

order12231
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#16861375

Splittings

FittingC3×C9×C151 ⋊ C3
SylowC151 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C151⋊C3
commutator, cosocleC3×C151C33
FrattiniC3C32×C151⋊C3
FittingC3×C9×C151C3
socleC32×C151C32
prime radicalC32×C151⋊C3C3
hypercenterC3×C9C151⋊C3
hypocenterC151C3×3−1+2
LCSG ▷ C3×C151 ▷ C151
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1383 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#16861375⋊C9, C9×#16861375, #49144493, …
maximal normal subgroup of#16861375⋊C9, C9×#16861375, #49144493, …
maximal quotient ofC3×(C3×C151⋊C3)⋊C9, C3×(C151⋊C9)⋊C9, C3×#27133546, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12231, 44);