Finite Group Databasebeta

← Prev (#28357336) Next (#28357338) →

C4×C11⋊C5×C7⋊C9 #28357337

order13860
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11⋊C5×C7⋊C9
unambiguous semidirect product(C4×C7)⋊(C9×C11⋊C5)
unambiguous semidirect product(C4×C11)⋊(C5×C7⋊C9)
unambiguous semidirect product(C4×C7×C11⋊C5)⋊C9
unambiguous semidirect product(C4×C11×C7⋊C9)⋊C5

Splittings

derived, HallC7×C11 ⋊ C4×C5×C9
HallC4×C11×C7⋊C9 ⋊ C5
HallC4×C7×C11⋊C5 ⋊ C9
HallC11×C7⋊C9 ⋊ C4×C5
HallC7×C11⋊C5 ⋊ C4×C9
HallC4×C7×C11 ⋊ C5×C9
HallC4×C11 ⋊ C5×C7⋊C9
HallC4×C7 ⋊ C9×C11⋊C5
SylowC11 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C4×C9×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3×C4ΓL(1,𝔽8)×C11⋊C5
commutator, hypocenterC7×C11C4×C5×C9
FrattiniC2×C3C2×ΓL(1,𝔽8)×C11⋊C5
FittingC3×C4×C7×C11C3×C5
socle, cosocleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×C7×C11⋊C5C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 4);