Finite Group Databasebeta

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C9×C7⋊(C11⋊#261) #49114459

order36036
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊(C11⋊#261)
unambiguous semidirect productC11⋊(C9×C7⋊#261)

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C4
derived, HallC7×C11×C13 ⋊ C4×C9
HallC9×C11×C13 ⋊ Dic7
HallC7×C9×C13 ⋊ Dic11
HallC7×C9×C11 ⋊ #261
HallC11×C13 ⋊ C9×Dic7
HallC9×C13 ⋊ Dic77
HallC9×C11 ⋊ C7⋊#261
HallC7×C13 ⋊ C9×Dic11
HallC7×C11 ⋊ C9×#261
HallC7×C9 ⋊ C11⋊#261
SylowC13 ⋊ C9×Dic77
SylowC11 ⋊ C9×C7⋊#261
SylowC7 ⋊ C9×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC9C7⋊(C11⋊#261)
commutator, hypocenterC7×C11×C13C4×C9
FrattiniC3C3×C7⋊(C11⋊#261)
FittingC7×C9×C11×C13C4
socleC3×C7×C11×C13C3×C4
prime radical, cosocleC3×C7×C11×D13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

2799 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 127);