Finite Group Databasebeta

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C5×C9×C101⋊C5 #36384367

order22725
automorphism?
homologyAbelianization (H1) = C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×C9×C101⋊C5
unambiguous semidirect productC101⋊(C52×C9)
unambiguous semidirect product(C5×C101)⋊(C5×C9)
unambiguous semidirect product(C9×C101)⋊C52
unambiguous semidirect product(C5×C9×C101)⋊C5

Splittings

FittingC5×C9×C101 ⋊ C5
derived, SylowC101 ⋊ C52×C9
HallC9×C101 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C9C101⋊C5
commutator, hypocenterC101C52×C9
FrattiniC3C3×C5×C101⋊C5
FittingC5×C9×C101C5
socleC3×C5×C101C3×C5
prime radicalC3×C5×C101⋊C5C3
cosocleC3×C101C3×C52
LCSG ▷ C101
UCSC1 ◁ C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4545

Conjugacy classes & character table

1125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22725, 7);