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C5×C9⋊(C11⋊#261) #38787882

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

Aliases

direct productC5×C9⋊(C11⋊#261)
unambiguous semidirect productC9⋊(C5×C11⋊#261)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C4
derived, HallC9×C11×C13 ⋊ C4×C5
HallC5×C11×C13 ⋊ Dic9
HallC5×C9×C13 ⋊ Dic11
HallC5×C9×C11 ⋊ #261
HallC11×C13 ⋊ C5×Dic9
HallC9×C13 ⋊ C5×Dic11
HallC9×C11 ⋊ C5×#261
HallC5×C13 ⋊ Dic99
HallC5×C11 ⋊ C9⋊#261
HallC5×C9 ⋊ C11⋊#261
SylowC13 ⋊ C5×Dic99
SylowC11 ⋊ C5×C9⋊#261
SylowC9 ⋊ C5×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC5C9⋊(C11⋊#261)
commutator, hypocenterC9×C11×C13C4×C5
FrattiniC3C5×C3⋊(C11⋊#261)
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13Dic3
prime radicalC3×C5×C11×D13D3
cosocleC9×C11×D13C2×C5
LCSG ▷ C9×C11×C13
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 113);