Finite Group Databasebeta

← Prev (#38737330) Next (#38737332) →

C7×C23×AGL(1,𝔽13) #38737331

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC7×C13×C23 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C7×C23
HallC7×C23×#261 ⋊ C3
HallC7×C23×C13⋊C3 ⋊ C4
HallC23×#261 ⋊ C3×C7
HallC23×C13⋊C3 ⋊ C4×C7
HallC7×#261 ⋊ C3×C23
HallC13×C23 ⋊ C3×C4×C7
HallC7×C13⋊C3 ⋊ C4×C23
HallC7×C13 ⋊ C3×C4×C23
Hall#261 ⋊ C3×C7×C23
HallC13⋊C3 ⋊ C4×C7×C23

Subgroups

subgroupG/H
center, hypercenterC7×C23AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C7×C23
FrattiniC1G
Fitting, socleC7×C13×C23C3×C4
prime radicalC7×C23×D13⋊C3C2
cosocleD13C2×C3×C7×C23
LCSG ▷ C13
UCSC1 ◁ C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

2093 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 50);