Finite Group Databasebeta

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C32×C4×C131⋊C5 #37556070

order23580
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C4×C131⋊C5
unambiguous semidirect product(C4×C131)⋊(C32×C5)
unambiguous semidirect product(C3×C4×C131)⋊(C3×C5)
unambiguous semidirect product(C32×C4×C131)⋊C5

Splittings

Fitting, HallC32×C4×C131 ⋊ C5
derived, SylowC131 ⋊ C32×C4×C5
HallC32×C131 ⋊ C4×C5
HallC4×C131 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32×C4C131⋊C5
commutator, hypocenterC131C32×C4×C5
FrattiniC2C2×C32×C131⋊C5
FittingC32×C4×C131C5
socleC2×C32×C131C2×C5
prime radicalC2×C32×C131⋊C5C2
cosocleC2×C131C2×C32×C5
LCSG ▷ C131
UCSC1 ◁ C32×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4716

Conjugacy classes & character table

1116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 45);