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C4×C52×C31⋊C9 #42124365

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

Aliases

direct productC4×C52×C31⋊C9

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C4×C52C31⋊C3
commutator, hypocenterC31C4×C52×C9
FrattiniC2×C3C2×C52×C31⋊C3
FittingC3×C4×C52×C31C3
socle, prime radicalC2×C3×C52×C31C2×C3
cosocleC2×C3×C31C2×C3×C52
LCSG ▷ C31
UCSC1 ◁ C3×C4×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 112);