Finite Group Databasebeta

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C4×C71×C37⋊C3 #44538600

order31524
automorphism?
homologyAbelianization (H1) = C3×C4×C71 · Schur multiplier (H2) = C1

Aliases

direct productC4×C71×C37⋊C3
unambiguous semidirect product(C4×C37)⋊(C3×C71)
unambiguous semidirect product(C4×C37×C71)⋊C3

Splittings

Fitting, HallC4×C37×C71 ⋊ C3
derived, SylowC37 ⋊ C3×C4×C71
HallC37×C71 ⋊ C3×C4
HallC4×C37 ⋊ C3×C71

Subgroups

subgroupG/H
center, hypercenterC4×C71C37⋊C3
commutator, hypocenterC37C3×C4×C71
FrattiniC2C2×C71×C37⋊C3
FittingC4×C37×C71C3
socleC2×C37×C71C2×C3
prime radicalC2×C71×C37⋊C3C2
cosocleC2×C37C2×C3×C71
LCSG ▷ C37
UCSC1 ◁ C4×C71

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10508

Conjugacy classes & character table

4260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31524, 2);