Finite Group Databasebeta

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C31×C3⋊(#1043⋊C3) #42124785

order27900
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×C3⋊(#1043⋊C3)
unambiguous semidirect productC3⋊(C31×#1043⋊C3)
unambiguous semidirect product(C3⋊#1043)⋊(C3×C31)

Splittings

Fitting, socleC3×C52×C31 ⋊ C3×C4
derivedC3×C52 ⋊ C3×C4×C31
HallC3×C31×C52⋊C3 ⋊ C4
HallC52×C31 ⋊ C3×Dic3
HallC3×C52⋊C3 ⋊ C4×C31
SylowC52 ⋊ C3×Dic3×C31

Subgroups

subgroupG/H
center, hypercenterC31C3⋊(#1043⋊C3)
commutator, hypocenterC3×C52C3×C4×C31
FrattiniC1G
Fitting, socleC3×C52×C31C3×C4
prime radicalC3×C31×(C5⋊D5)⋊C3C2
cosocleC3×C5⋊D5C2×C3×C31
LCSG ▷ C3×C52
UCSC1 ◁ C31

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

744 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 532);