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C4×C31×C52⋊C9 #42124366

order27900
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C5

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C4×C31C52⋊C3
commutator, hypocenterC52C4×C9×C31
FrattiniC2×C3C2×C31×C52⋊C3
FittingC3×C4×C52×C31C3
socle, prime radicalC2×C3×C52×C31C2×C3
cosocleC2×C3×C52C2×C3×C31
LCSG ▷ C52
UCSC1 ◁ C3×C4×C31

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 113);