Finite Group Databasebeta

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C4×C9×C31⋊C25 #42124263

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

Aliases

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

Splittings

derived, SylowC31 ⋊ C4×C9×C25
HallC4×C9×C31 ⋊ C25
HallC9×C31 ⋊ C4×C25
HallC4×C31 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC4×C5×C9ΓL(1,𝔽32)
commutator, hypocenterC31C4×C9×C25
FrattiniC2×C3×C5C2×C3×ΓL(1,𝔽32)
FittingC4×C5×C9×C31C5
socle, prime radical, cosocleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C4×C5×C9

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 10);