Finite Group Databasebeta

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C3×C4×C113⋊C7 #23748760

order9492
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C113⋊C7
unambiguous semidirect product(C4×C113)⋊(C3×C7)
unambiguous semidirect product(C3×C4×C113)⋊C7

Splittings

Fitting, HallC3×C4×C113 ⋊ C7
derived, SylowC113 ⋊ C3×C4×C7
HallC4×C113 ⋊ C3×C7
HallC3×C113 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4C113⋊C7
commutator, hypocenterC113C3×C4×C7
FrattiniC2C2×C3×C113⋊C7
FittingC3×C4×C113C7
socleC2×C3×C113C2×C7
prime radicalC2×C3×C113⋊C7C2
cosocleC2×C113C2×C3×C7
LCSG ▷ C113
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C9×C113⋊C7, C3×Dic3×C113⋊C7, C32×C4×C113⋊C7
maximal normal subgroup ofC4×C9×C113⋊C7, C32×C4×C113⋊C7
maximal quotient ofC4×C9×C113⋊C7, C3×Dic3×C113⋊C7, C32×C4×C113⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9492, 2);