Finite Group Databasebeta

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C3×C7×C11⋊AGL(1,𝔽13) #49114637

order36036
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×C11⋊AGL(1,𝔽13)
unambiguous semidirect productC11⋊(C3×C7×AGL(1,𝔽13))
unambiguous semidirect product(C11⋊#261)⋊(C32×C7)
unambiguous semidirect product(C3×C11⋊#261)⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3×C4
derived, HallC11×C13 ⋊ C32×C4×C7
HallC3×C7×C11×C13⋊C3 ⋊ C4
HallC7×C11⋊#261 ⋊ C32
HallC3×C11×C13⋊C3 ⋊ C4×C7
HallC7×C11×C13 ⋊ C32×C4
HallC3×C7×C13⋊C3 ⋊ Dic11
HallC11⋊#261 ⋊ C32×C7
HallC3×C13⋊C3 ⋊ C7×Dic11
HallC7×C13 ⋊ C32×Dic11
HallC7×C11 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C32×C7×Dic11
SylowC11 ⋊ C3×C7×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC3×C7C11⋊AGL(1,𝔽13)
commutator, hypocenterC11×C13C32×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3×C4
prime radicalC3×C7×C11×D13⋊C3C2
cosocleC11×D13C2×C32×C7
LCSG ▷ C11×C13
UCSC1 ◁ C3×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 305);