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A5×(C31⋊C3)⋊C5 #42124998

order27900
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productA5×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C5×A5)
unambiguous semidirect productΓL(1,𝔽32)⋊(C3×A5)
unambiguous semidirect product(A5×C31⋊C3)⋊C5
unambiguous semidirect product(A5×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, SylowC31 ⋊ C3×C5×A5
socle, derivedC31×A5 ⋊ C3×C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, hypocenterC31×A5C3×C5
Fitting, cosocleC31C3×C5×A5
LCSG ▷ C31×A5
UCSC1

92 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 745);