Finite Group Databasebeta

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C22×C9×C131⋊C5 #37556044

order23580
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C9×C131⋊C5
unambiguous semidirect product(C22×C9×C131)⋊C5

Splittings

Fitting, HallC22×C9×C131 ⋊ C5
derived, SylowC131 ⋊ C22×C5×C9
HallC9×C131 ⋊ C22×C5
HallC22×C131 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC22×C9C131⋊C5
commutator, hypocenterC131C22×C5×C9
FrattiniC3C22×C3×C131⋊C5
FittingC22×C9×C131C5
socleC22×C3×C131C3×C5
prime radicalC22×C3×C131⋊C5C3
cosocleC3×C131C22×C3×C5
LCSG ▷ C131
UCSC1 ◁ C22×C9

60 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, 19);