Finite Group Databasebeta

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C3×C7×C11×AGL(1,𝔽13) #49114636

order36036
automorphism?
homologyAbelianization (H1) = C32×C4×C7×C11 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3×C4
derived, SylowC13 ⋊ C32×C4×C7×C11
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 ⋊ C4×C11
HallC11×#261 ⋊ C32×C7
HallC7×#261 ⋊ C32×C11
HallC11×C13 ⋊ C32×C4×C7
HallC3×C13⋊C3 ⋊ C4×C7×C11
HallC7×C13 ⋊ C32×C4×C11
Hall#261 ⋊ C32×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11AGL(1,𝔽13)
commutator, hypocenterC13C32×C4×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3×C4
prime radicalC3×C7×C11×D13⋊C3C2
cosocleD13C2×C32×C7×C11
LCSG ▷ C13
UCSC1 ◁ C3×C7×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 304);