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C2×C3×C5×(C31⋊C3)⋊C5 #28358459

order13950
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC2×C3×C5×(C31⋊C3)⋊C5
unambiguous semidirect product(C2×C31⋊C3)⋊(C3×C52)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C32×C5)
unambiguous semidirect product(C2×C3×C31⋊C3)⋊C52
unambiguous semidirect product(C2×C3×ΓL(1,𝔽32))⋊(C3×C5)
unambiguous semidirect product(C2×C5×C31⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C5×ΓL(1,𝔽32))⋊C32
unambiguous semidirect product(C2×C3×C5×C31⋊C3)⋊C5
unambiguous semidirect product(C2×C3×C5×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socleC2×C3×C5×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C2×C32×C52
HallC2×C5×ΓL(1,𝔽32) ⋊ C32
HallC5×ΓL(1,𝔽32) ⋊ C2×C32
HallC2×C3×C31⋊C3 ⋊ C52
HallC3×C31⋊C3 ⋊ C2×C52
HallC2×C31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C2×C32×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

510 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×((C31⋊C3)⋊C4)⋊C5, C3×((C31⋊C3)⋊C5)⋊Dic5, C3×Dic5×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC3×C5×((C31⋊C3)⋊C4)⋊C5, C3×((C31⋊C3)⋊C5)⋊Dic5, C3×Dic5×(C31⋊C3)⋊C5, …
maximal quotient ofC3×C4×C5×(C31⋊C3)⋊C5, C22×C3×C5×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 102);