Finite Group Databasebeta

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C7×C9×D187 #37555611

order23562
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×D187
unambiguous semidirect productC11⋊(C7×C9×D17)
unambiguous semidirect productC17⋊(C7×C9×D11)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC11×C17 ⋊ C2×C7×C9
HallC9×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C2×C9
HallC7×C9×C17 ⋊ D11
HallC7×C9×C11 ⋊ D17
HallC9×C17 ⋊ C7×D11
HallC7×C17 ⋊ C9×D11
HallC9×C11 ⋊ C7×D17
HallC7×C11 ⋊ C9×D17
SylowC17 ⋊ C7×C9×D11
SylowC11 ⋊ C7×C9×D17

Subgroups

subgroupG/H
center, hypercenterC7×C9D187
commutator, hypocenterC11×C17C2×C7×C9
FrattiniC3C3×C7×D187
FittingC7×C9×C11×C17C2
socleC3×C7×C11×C17C2×C3
prime radicalC3×C7×D187C3
cosocleC3×C11×C17C2×C3×C7
LCSG ▷ C11×C17
UCSC1 ◁ C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5985 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 5);