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C52×#261⋊C9 #26043348

order11700
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C4×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC52×#261⋊C9
unambiguous semidirect product#261⋊(C52×C9)
unambiguous semidirect product(C5×#261)⋊(C5×C9)

Splittings

derived, SylowC13 ⋊ C4×C52×C9
HallC52×C13⋊C9 ⋊ C4
HallC52×#261 ⋊ C9
HallC52×C13 ⋊ C4×C9
HallC13⋊C9 ⋊ C4×C52
Hall#261 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC3×C52AGL(1,𝔽13)
commutator, hypocenterC13C4×C52×C9
FrattiniC3C52×AGL(1,𝔽13)
Fitting, socleC3×C52×C13C3×C4
prime radicalC3×C52×D13C2×C3
cosocleC3×D13C2×C3×C52
LCSG ▷ C13
UCSC1 ◁ C3×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 195);