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C9×D2093 #49179129

order37674
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D2093
unambiguous semidirect productC23⋊(C9×D91)

Splittings

Fitting, HallC7×C9×C13×C23 ⋊ C2
derived, HallC7×C13×C23 ⋊ C2×C9
HallC9×C13×C23 ⋊ D7
HallC7×C9×C23 ⋊ D13
HallC7×C9×C13 ⋊ D23
HallC13×C23 ⋊ C9×D7
HallC9×C23 ⋊ D91
HallC7×C23 ⋊ C9×D13
HallC9×C13 ⋊ D161
HallC7×C13 ⋊ C9×D23
HallC7×C9 ⋊ D299
SylowC23 ⋊ C9×D91
SylowC13 ⋊ C9×D161
SylowC7 ⋊ C9×D299

Subgroups

subgroupG/H
center, hypercenterC9D2093
commutator, hypocenterC7×C13×C23C2×C9
FrattiniC3C3×D2093
FittingC7×C9×C13×C23C2
socle, cosocleC3×C7×C13×C23C2×C3
prime radicalC3×D2093C3
LCSG ▷ C7×C13×C23
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18837

Conjugacy classes & character table

9432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37674, 12);