Finite Group Databasebeta

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C11×C17⋊(D7⋊C9) #37555628

order23562
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17⋊(D7⋊C9)
unambiguous semidirect productC17⋊(C11×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C11×D17)
unambiguous semidirect productD119⋊(C9×C11)
unambiguous semidirect product(C11×D119)⋊C9

Splittings

derived, HallC7×C17 ⋊ C2×C9×C11
HallC11×C17×C7⋊C9 ⋊ C2
HallC11×D119 ⋊ C9
HallC7×C11×C17 ⋊ C2×C9
HallC17×C7⋊C9 ⋊ C2×C11
HallC11×C7⋊C9 ⋊ D17
HallD119 ⋊ C9×C11
HallC11×C17 ⋊ D7⋊C9
HallC7×C11 ⋊ C9×D17
HallC7⋊C9 ⋊ C11×D17
SylowC17 ⋊ C11×D7⋊C9
SylowC7 ⋊ C9×C11×D17

Subgroups

subgroupG/H
center, hypercenterC3×C11C17⋊AGL(1,𝔽7)
commutator, hypocenterC7×C17C2×C9×C11
FrattiniC3C11×C17⋊AGL(1,𝔽7)
Fitting, socleC3×C7×C11×C17C2×C3
prime radicalC3×C11×D119C3
cosocleC3×C7×C17C2×C3×C11
LCSG ▷ C7×C17
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

1551 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 22);