Finite Group Databasebeta

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C2×C9×C271⋊C5 #37567243

order24390
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×C271⋊C5
unambiguous semidirect product(C2×C9×C271)⋊C5

Splittings

Fitting, HallC2×C9×C271 ⋊ C5
derived, SylowC271 ⋊ C2×C5×C9
HallC9×C271 ⋊ C2×C5
HallC2×C271 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9C271⋊C5
commutator, hypocenterC271C2×C5×C9
FrattiniC3C2×C3×C271⋊C5
FittingC2×C9×C271C5
socleC2×C3×C271C3×C5
prime radicalC2×C3×C271⋊C5C3
cosocleC3×C271C2×C3×C5
LCSG ▷ C271
UCSC1 ◁ C2×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4878

Conjugacy classes & character table

1062 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24390, 2);