Finite Group Databasebeta

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C4×C25×C31⋊C9 #42124264

order27900
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, SylowC31 ⋊ C4×C9×C25
HallC4×C25×C31 ⋊ C9
HallC25×C31 ⋊ C4×C9
HallC4×C31 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C4×C25C31⋊C3
commutator, hypocenterC31C4×C9×C25
FrattiniC2×C3×C5C2×C5×C31⋊C3
FittingC3×C4×C25×C31C3
socle, prime radical, cosocleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C4×C25

54 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, 11);