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C121×AGL(1,𝔽13) #34038332

order18876
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productC121×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C121)
unambiguous semidirect product(#261×C121)⋊C3

Splittings

Fitting, HallC13×C121 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C121
Hall#261×C121 ⋊ C3
HallC13⋊C3×C121 ⋊ C4
Hall#261 ⋊ C3×C121
HallC13⋊C3 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC121AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C121
FrattiniC11C11×AGL(1,𝔽13)
FittingC13×C121C3×C4
socleC11×C13C3×C4×C11
prime radicalC11×D13⋊C3C2×C11
cosocleC11×D13C2×C3×C11
LCSG ▷ C13
UCSC1 ◁ C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1573

Conjugacy classes & character table

1573 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 14);