Finite Group Databasebeta

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C3×(C31⋊C3)⋊#1044 #42124764

order27900
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×(C31⋊C3)⋊#1044
unambiguous semidirect product(C31⋊C3)⋊(C3×#1044)
unambiguous semidirect product(C31⋊#1044)⋊C32
unambiguous semidirect product(C3×C31⋊#1044)⋊C3

Splittings

Fitting, socleC3×C52×C31 ⋊ C3×C4
derived, HallC52×C31 ⋊ C32×C4
HallC3×C52×C31⋊C3 ⋊ C4
HallC31⋊#1044 ⋊ C32
HallC3×C31⋊C3 ⋊ #1044
SylowC31 ⋊ C32×#1044
SylowC52 ⋊ C3×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC3(C31⋊C3)⋊#1044
commutator, hypocenterC52×C31C32×C4
FrattiniC1G
Fitting, socleC3×C52×C31C3×C4
prime radicalC3×C5⋊D5×C31⋊C3C2
cosocleC31×C5⋊D5C2×C32
LCSG ▷ C52×C31
UCSC1 ◁ C3

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

300 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 511);