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C5×A4×(C31⋊C3)⋊C5 #42124681

order27900
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC5×A4×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C52×A4)
unambiguous semidirect product(C5×C31⋊C3)⋊(C5×A4)
unambiguous semidirect product(A4×C31⋊C3)⋊C52
unambiguous semidirect product(C22×(C31⋊C3)⋊C5)⋊(C3×C5)
unambiguous semidirect product(A4×ΓL(1,𝔽32))⋊(C3×C5)
unambiguous semidirect product(C22⋊((C31⋊C3)⋊C5))⋊(C3×C5)
unambiguous semidirect product(C5×A4×C31⋊C3)⋊C5
unambiguous semidirect product(C22×C5×(C31⋊C3)⋊C5)⋊C3
unambiguous semidirect product(C5×C22⋊((C31⋊C3)⋊C5))⋊C3
unambiguous semidirect product(C5×A4×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC22×C5×C31 ⋊ C32×C5
derived, HallC22×C31 ⋊ C32×C52
HallC22×C5×ΓL(1,𝔽32) ⋊ C32
HallA4×C31⋊C3 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C3×A4
SylowC31 ⋊ C3×C52×A4
SylowC22 ⋊ C3×C5×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC5A4×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC22×C31C32×C52
FrattiniC1G
Fitting, socleC22×C5×C31C32×C5
LCSG ▷ C22×C31
UCSC1 ◁ C5

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 428);