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C3×C22⋊(C52⋊(C31⋊C3)) #42124974

order27900
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC3×C22⋊(C52⋊(C31⋊C3))
unambiguous semidirect product(C22×C3)⋊(C52⋊(C31⋊C3))
unambiguous semidirect product(C3×C52)⋊(C22⋊(C31⋊C3))
unambiguous semidirect product(C3×C31)⋊(C22⋊(C52⋊C3))

Splittings

Fitting, socleC22×C3×C52×C31 ⋊ C3
derived, HallC22×C52×C31 ⋊ C32
HallC52×C31 ⋊ C3×A4
HallC22×C31 ⋊ C3×C52⋊C3
HallC22×C52 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×C22⋊(C52⋊C3)
SylowC52 ⋊ C3×C22⋊(C31⋊C3)
SylowC22 ⋊ C3×C52⋊(C31⋊C3)

Subgroups

subgroupG/H
center, hypercenterC3C22⋊(C52⋊(C31⋊C3))
commutator, cosocle, hypocenterC22×C52×C31C32
FrattiniC1G
Fitting, socleC22×C3×C52×C31C3
LCSG ▷ C22×C52×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 721);