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C9×Dic11×C89 #47976458

order35244
automorphism?
homologyAbelianization (H1) = C4×C9×C89 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic11×C89
unambiguous semidirect productC11⋊(C4×C9×C89)

Splittings

derived, SylowC11 ⋊ C4×C9×C89
HallC9×C11×C89 ⋊ C4
HallC11×C89 ⋊ C4×C9
HallC9×C11 ⋊ C4×C89

Subgroups

subgroupG/H
center, hypercenterC2×C9×C89D11
commutator, hypocenterC11C4×C9×C89
FrattiniC2×C3C3×D11×C89
FittingC2×C9×C11×C89C2
socle, prime radicalC2×C3×C11×C89C2×C3
cosocleC2×C3×C11C2×C3×C89
LCSG ▷ C11
UCSC1 ◁ C2×C9×C89

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35244

Conjugacy classes & character table

11214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35244, 4);