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C5×C3⋊(C3⋊(D31⋊C5)) #28358467

order13950
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC5×C3⋊(C3⋊(D31⋊C5))
unambiguous semidirect productC3⋊(C5×C3⋊(D31⋊C5))
unambiguous semidirect productΓL(1,𝔽32)⋊(C5×C3⋊D3)
unambiguous semidirect product(C3⋊D93)⋊C52
unambiguous semidirect product(C5×C3⋊D93)⋊C5

Splittings

Fitting, socleC32×C5×C31 ⋊ C2×C5
derived, HallC32×C31 ⋊ C2×C52
HallC32×C5×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C3⋊D3
HallC3⋊D93 ⋊ C52
SylowC31 ⋊ C52×C3⋊D3
SylowC32 ⋊ C5×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊(D31⋊C5))
commutator, cosocle, hypocenterC32×C31C2×C52
FrattiniC1G
Fitting, socleC32×C5×C31C2×C5
LCSG ▷ C32×C31
UCSC1 ◁ C5

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

285 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×C3⋊(D31⋊C5), D15⋊(C3⋊(D31⋊C5)), C5×C3⋊D3×D31⋊C5, …
maximal normal subgroup ofC5×D3×C3⋊(D31⋊C5), D15⋊(C3⋊(D31⋊C5)), C5×C3⋊D3×D31⋊C5, …
maximal quotient ofC5×C3⋊(C3⋊(Dic31⋊C5)), C2×C5×C3⋊(C3⋊(D31⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 110);