Finite Group Databasebeta

← Prev (#26043261) Next (#26043263) →

C25×C3⋊AGL(1,𝔽13) #26043262

order11700
isoclinismisoclinic class of C3⋊AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×C3⋊AGL(1,𝔽13)
unambiguous semidirect productC3⋊(C25×AGL(1,𝔽13))
unambiguous semidirect product(C3⋊#261)⋊(C3×C25)
unambiguous semidirect product(C25×C3⋊#261)⋊C3

Splittings

FittingC3×C13×C25 ⋊ C3×C4
derivedC3×C13 ⋊ C3×C4×C25
HallC3×C25×C13⋊C3 ⋊ C4
HallC13×C25 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C25
SylowC13 ⋊ C3×Dic3×C25

Subgroups

subgroupG/H
center, hypercenterC25C3⋊AGL(1,𝔽13)
commutator, hypocenterC3×C13C3×C4×C25
FrattiniC5C5×C3⋊AGL(1,𝔽13)
FittingC3×C13×C25C3×C4
socleC3×C5×C13C3×C4×C5
prime radicalC3×C5×D13⋊C3C2×C5
cosocleC3×C5×D13C2×C3×C5
LCSG ▷ C3×C13
UCSC1 ◁ C25

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 109);