Finite Group Databasebeta

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C11×C22⋊(C67⋊C9) #40997609

order26532
automorphism?
homologyAbelianization (H1) = C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×C22⋊(C67⋊C9)
unambiguous semidirect productC22⋊(C11×C67⋊C9)
unambiguous semidirect product(C22×C11)⋊(C67⋊C9)
unambiguous semidirect product(C11×C67)⋊(C22⋊C9)

Splittings

derived, HallC22×C67 ⋊ C9×C11
HallC22×C11×C67 ⋊ C9
HallC11×C67 ⋊ C22⋊C9
SylowC67 ⋊ C11×C22⋊C9
HallC22×C11 ⋊ C67⋊C9
SylowC22 ⋊ C11×C67⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C11C22⋊(C67⋊C3)
commutator, hypocenterC22×C67C9×C11
FrattiniC3C11×C22⋊(C67⋊C3)
Fitting, socle, prime radicalC22×C3×C11×C67C3
cosocleC22×C3×C67C3×C11
LCSG ▷ C22×C67
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13266

Conjugacy classes & character table

3036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26532, 40);