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C4×C52⋊(C31⋊C9) #42124367

order27900
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊(C31⋊C9)
unambiguous semidirect product(C4×C52)⋊(C31⋊C9)
unambiguous semidirect product(C4×C31)⋊(C52⋊C9)

Splittings

derived, HallC52×C31 ⋊ C4×C9
HallC4×C52×C31 ⋊ C9
HallC4×C31 ⋊ C52⋊C9
HallC4×C52 ⋊ C31⋊C9
SylowC31 ⋊ C4×C52⋊C9
SylowC52 ⋊ C4×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C4C52⋊(C31⋊C3)
commutator, hypocenterC52×C31C4×C9
FrattiniC2×C3C2×C52⋊(C31⋊C3)
FittingC3×C4×C52×C31C3
socle, prime radical, cosocleC2×C3×C52×C31C2×C3
LCSG ▷ C52×C31
UCSC1 ◁ C3×C4

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 114);