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C3×C4×C52⋊(C31⋊C3) #42124649

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

Aliases

direct productC3×C4×C52⋊(C31⋊C3)
unambiguous semidirect product(C3×C4×C52)⋊(C31⋊C3)
unambiguous semidirect product(C3×C4×C31)⋊(C52⋊C3)

Splittings

FittingC3×C4×C52×C31 ⋊ C3
derived, HallC52×C31 ⋊ C32×C4
HallC4×C52×C31 ⋊ C32
HallC4×C31 ⋊ C3×C52⋊C3
HallC4×C52 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×C4×C52⋊C3
SylowC52 ⋊ C3×C4×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C4C52⋊(C31⋊C3)
commutator, hypocenterC52×C31C32×C4
FrattiniC2C2×C3×C52⋊(C31⋊C3)
FittingC3×C4×C52×C31C3
socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C52⋊(C31⋊C3)C2
cosocleC2×C52×C31C2×C32
LCSG ▷ C52×C31
UCSC1 ◁ C3×C4

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3132 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 396);