Finite Group Databasebeta

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C3×C31⋊C3×#1035 #42124396

order27900
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C31⋊C3×#1035
unambiguous semidirect product(C31×#1035)⋊C32
unambiguous semidirect product(C3×C31×#1035)⋊C3

Splittings

FittingC3×C25×C31 ⋊ C3×C4
derived, HallC25×C31 ⋊ C32×C4
HallC3×C25×C31⋊C3 ⋊ C4
HallC31×#1035 ⋊ C32
SylowC31 ⋊ C32×#1035
SylowC25 ⋊ C3×C4×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C31⋊C3×#1035
commutator, hypocenterC25×C31C32×C4
FrattiniC5C3×AGL(1,𝔽5)×C31⋊C3
FittingC3×C25×C31C3×C4
socleC3×C5×C31C3×AGL(1,𝔽5)
prime radicalC3×D25×C31⋊C3C2
cosocleC31×D25C2×C32
LCSG ▷ C25×C31
UCSC1 ◁ C3

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 143);