Finite Group Databasebeta

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C5×C11⋊(#261⋊C9) #38787828

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(#261⋊C9)
unambiguous semidirect product(C5×C11⋊#261)⋊C9

Splittings

derived, HallC11×C13 ⋊ C4×C5×C9
HallC5×C11×C13⋊C9 ⋊ C4
HallC5×C11⋊#261 ⋊ C9
HallC11×C13⋊C9 ⋊ C4×C5
HallC5×C11×C13 ⋊ C4×C9
HallC5×C13⋊C9 ⋊ Dic11
HallC11⋊#261 ⋊ C5×C9
HallC13⋊C9 ⋊ C5×Dic11
HallC5×C13 ⋊ C9×Dic11
HallC5×C11 ⋊ #261⋊C9
SylowC13 ⋊ C5×C9×Dic11
SylowC11 ⋊ C5×#261⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊AGL(1,𝔽13)
commutator, hypocenterC11×C13C4×C5×C9
FrattiniC3C5×C11⋊AGL(1,𝔽13)
Fitting, socleC3×C5×C11×C13C3×C4
prime radicalC3×C5×C11×D13C2×C3
cosocleC3×C11×D13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

795 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 59);