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C7×C23⋊AGL(1,𝔽13) #38737332

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23⋊AGL(1,𝔽13)
unambiguous semidirect productC23⋊(C7×AGL(1,𝔽13))
unambiguous semidirect product(C23⋊#261)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C23 ⋊ C3×C4
derived, HallC13×C23 ⋊ C3×C4×C7
HallC7×C23⋊#261 ⋊ C3
HallC7×C23×C13⋊C3 ⋊ C4
HallC23⋊#261 ⋊ C3×C7
HallC23×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ Dic23
HallC7×C23 ⋊ AGL(1,𝔽13)
HallC7×C13 ⋊ C3×Dic23
HallC13⋊C3 ⋊ C7×Dic23
SylowC23 ⋊ C7×AGL(1,𝔽13)
SylowC13 ⋊ C3×C7×Dic23

Subgroups

subgroupG/H
center, hypercenterC7C23⋊AGL(1,𝔽13)
commutator, hypocenterC13×C23C3×C4×C7
FrattiniC1G
Fitting, socleC7×C13×C23C3×C4
prime radicalC7×C23×D13⋊C3C2
cosocleC23×D13C2×C3×C7
LCSG ▷ C13×C23
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 51);