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D5×ΓL(1,𝔽32)⋊C9 #28358409

order13950
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽32)⋊C9
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽32)⋊C9)
unambiguous semidirect product(D5×ΓL(1,𝔽32))⋊C9
unambiguous semidirect product(D5×C31⋊C9)⋊C5

Splittings

derivedC5×C31 ⋊ C2×C5×C9
HallC5×ΓL(1,𝔽32)⋊C9 ⋊ C2
HallD5×ΓL(1,𝔽32) ⋊ C9
HallC5×ΓL(1,𝔽32) ⋊ C2×C9
HallC31⋊C9 ⋊ C5×D5
SylowC31 ⋊ C5×C9×D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC3D5×(C31⋊C3)⋊C5
commutator, hypocenterC5×C31C2×C5×C9
Fitting, socle, cosocleC3×C5×C31C2×C3×C5
prime radicalC3×D5×ΓL(1,𝔽32)C3
LCSG ▷ C5×C31
UCSC1 ◁ C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(ΓL(1,𝔽32)⋊C9)⋊AGL(1,𝔽5), AGL(1,𝔽5)×ΓL(1,𝔽32)⋊C9, D5×(D31⋊C5)⋊C9, …
maximal normal subgroup of(ΓL(1,𝔽32)⋊C9)⋊AGL(1,𝔽5), AGL(1,𝔽5)×ΓL(1,𝔽32)⋊C9, D5×(D31⋊C5)⋊C9, …
maximal quotient ofDic5×ΓL(1,𝔽32)⋊C9, C2×D5×ΓL(1,𝔽32)⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 52);