Finite Group Databasebeta

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C3×A4×C31⋊C25 #42124394

order27900
automorphism?
homologyAbelianization (H1) = C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C31⋊C25
unambiguous semidirect productC22⋊(C32×C31⋊C25)
unambiguous semidirect product(C22×C3)⋊(C3×C31⋊C25)
unambiguous semidirect product(C3×A4×C31)⋊C25

Splittings

derived, HallC22×C31 ⋊ C32×C25
HallC22×C31⋊C25 ⋊ C32
HallC3×A4×C31 ⋊ C25
SylowC31 ⋊ C3×A4×C25
SylowC22 ⋊ C32×C31⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5A4×ΓL(1,𝔽32)
commutator, hypocenterC22×C31C32×C25
FrattiniC5C3×A4×ΓL(1,𝔽32)
Fitting, socleC22×C3×C5×C31C3×C5
prime radicalC3×C5×A4×C31C5
cosocleC22×C5×C31C32×C5
LCSG ▷ C22×C31
UCSC1 ◁ C3×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 141);