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C11⋊C5×C22⋊(C7⋊C9) #28357384

order13860
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC11⋊C5×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C11⋊C5×C7⋊C9)
unambiguous semidirect productC7⋊(C22⋊C9×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C22⋊(C7⋊C9))
unambiguous semidirect product(C22×C11⋊C5)⋊(C7⋊C9)
unambiguous semidirect product(C7×C11⋊C5)⋊(C22⋊C9)
unambiguous semidirect product(C11×C22⋊(C7⋊C9))⋊C5

Splittings

derived, HallC22×C7×C11 ⋊ C5×C9
HallC11×C22⋊(C7⋊C9) ⋊ C5
HallC22×C7×C11⋊C5 ⋊ C9
HallC7×C11⋊C5 ⋊ C22⋊C9
HallC22×C11⋊C5 ⋊ C7⋊C9
HallC7×C11 ⋊ C5×C22⋊C9
HallC22×C11 ⋊ C5×C7⋊C9
HallC22×C7 ⋊ C9×C11⋊C5
SylowC11 ⋊ C5×C22⋊(C7⋊C9)
SylowC7 ⋊ C22⋊C9×C11⋊C5
SylowC22 ⋊ C11⋊C5×C7⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC3C11⋊C5×C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7×C11C5×C9
Fitting, socle, cosocleC22×C3×C7×C11C3×C5
prime radicalC22×C3×C7×C11⋊C5C3
LCSG ▷ C22×C7×C11
UCSC1 ◁ C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 51);