Finite Group Databasebeta

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C3×C25×C22⋊(C31⋊C3) #42124455

order27900
isoclinismisoclinic class of C22⋊(C31⋊C3)
automorphism?
homologyAbelianization (H1) = C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

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

Splittings

FittingC22×C3×C25×C31 ⋊ C3
derived, HallC22×C31 ⋊ C32×C25
HallC22×C25×C31 ⋊ C32
HallC25×C31 ⋊ C3×A4
HallC22×C25 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×A4×C25
SylowC22 ⋊ C3×C25×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C25C22⋊(C31⋊C3)
commutator, hypocenterC22×C31C32×C25
FrattiniC5C3×C5×C22⋊(C31⋊C3)
FittingC22×C3×C25×C31C3
socleC22×C3×C5×C31C3×C5
prime radicalC3×C5×C22⋊(C31⋊C3)C5
cosocleC22×C5×C31C32×C5
LCSG ▷ C22×C31
UCSC1 ◁ C3×C25

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 202);