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C5×(D31⋊C5)⋊C9 #28358407

order13950
automorphism?
homologyAbelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC5×(D31⋊C5)⋊C9
unambiguous semidirect product(D31⋊C5)⋊(C5×C9)
unambiguous semidirect product(D31⋊C9)⋊C52
unambiguous semidirect product(ΓL(1,𝔽32)⋊C9)⋊(C2×C5)
unambiguous semidirect product(C5×D31⋊C5)⋊C9
unambiguous semidirect product(C5×D31⋊C9)⋊C5

Splittings

derived, SylowC31 ⋊ C2×C52×C9
HallC5×ΓL(1,𝔽32)⋊C9 ⋊ C2
HallC5×D31⋊C5 ⋊ C9
HallC5×ΓL(1,𝔽32) ⋊ C2×C9
HallD31⋊C9 ⋊ C52
HallC31⋊C9 ⋊ C2×C52
HallD31 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5AGL(1,𝔽31)
commutator, hypocenterC31C2×C52×C9
FrattiniC3C5×AGL(1,𝔽31)
Fitting, socleC3×C5×C31C2×C3×C5
prime radicalC3×C5×D31⋊C5C3
cosocleC3×C31C2×C3×C52
LCSG ▷ C31
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

465 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×(D31⋊C5)⋊C9, C2×C5×(D31⋊C5)⋊C9
maximal normal subgroup ofD5×(D31⋊C5)⋊C9, C2×C5×(D31⋊C5)⋊C9
maximal quotient ofC5×(Dic31⋊C5)⋊C9, C2×C5×(D31⋊C5)⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 50);