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C4×(C31⋊C9)⋊C25 #42124256

order27900
automorphism?
homologyAbelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C31⋊C9)⋊C25
unambiguous semidirect product(C4×C31⋊C9)⋊C25
unambiguous semidirect product(C4×C31⋊C25)⋊C9

Splittings

derived, SylowC31 ⋊ C4×C9×C25
HallC4×C31⋊C25 ⋊ C9
HallC4×C31⋊C9 ⋊ C25
HallC31⋊C25 ⋊ C4×C9
HallC31⋊C9 ⋊ C4×C25
HallC4×C31 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5(C31⋊C3)⋊C5
commutator, hypocenterC31C4×C9×C25
FrattiniC2×C3×C5C2×(C31⋊C3)⋊C5
FittingC3×C4×C5×C31C3×C5
socle, prime radical, cosocleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C4×C5

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 3);