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C11×Dic531 #37552486

order23364
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic531
unambiguous semidirect productC9⋊(C11×Dic59)
unambiguous semidirect productC59⋊(C11×Dic9)

Splittings

derived, HallC9×C59 ⋊ C4×C11
HallC9×C11×C59 ⋊ C4
HallC11×C59 ⋊ Dic9
HallC9×C11 ⋊ Dic59
SylowC59 ⋊ C11×Dic9
SylowC9 ⋊ C11×Dic59

Subgroups

subgroupG/H
center, hypercenterC2×C11D531
commutator, hypocenterC9×C59C4×C11
FrattiniC2×C3C11×D177
FittingC2×C9×C11×C59C2
socle, prime radicalC2×C3×C11×C59D3
cosocleC2×C9×C59C2×C11
LCSG ▷ C9×C59
UCSC1 ◁ C2×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23364

Conjugacy classes & character table

5874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23364, 6);