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C3×C4×C5×(C31⋊C3)⋊C5 #42124606

order27900
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C4×C5×(C31⋊C3)⋊C5
unambiguous semidirect product(C4×C31⋊C3)⋊(C3×C52)
unambiguous semidirect product(C4×ΓL(1,𝔽32))⋊(C32×C5)
unambiguous semidirect product(C3×C4×C31⋊C3)⋊C52
unambiguous semidirect product(C3×C4×ΓL(1,𝔽32))⋊(C3×C5)
unambiguous semidirect product(C4×C5×C31⋊C3)⋊(C3×C5)
unambiguous semidirect product(C4×C5×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C3×C4×C5×C31⋊C3)⋊C5
unambiguous semidirect product(C3×C4×C5×ΓL(1,𝔽32))⋊C3

Splittings

FittingC3×C4×C5×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C32×C4×C52
HallC4×C5×ΓL(1,𝔽32) ⋊ C32
HallC3×C4×C31⋊C3 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C32×C4
HallC3×C31⋊C3 ⋊ C4×C52
HallC4×C31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5(C31⋊C3)⋊C5
commutator, hypocenterC31C32×C4×C52
FrattiniC2C2×C3×C5×(C31⋊C3)⋊C5
FittingC3×C4×C5×C31C3×C5
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C32×C52
LCSG ▷ C31
UCSC1 ◁ C3×C4×C5

288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 353);