Finite Group Databasebeta

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C7×D1683 #37555619

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

Aliases

direct productC7×D1683
unambiguous semidirect productC9⋊(C7×D187)
unambiguous semidirect productC11⋊(C7×D153)
unambiguous semidirect productC17⋊(C7×D99)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC9×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ D9
HallC7×C9×C17 ⋊ D11
HallC7×C9×C11 ⋊ D17
HallC11×C17 ⋊ C7×D9
HallC9×C17 ⋊ C7×D11
HallC7×C17 ⋊ D99
HallC9×C11 ⋊ C7×D17
HallC7×C11 ⋊ D153
HallC7×C9 ⋊ D187
SylowC17 ⋊ C7×D99
SylowC11 ⋊ C7×D153
SylowC9 ⋊ C7×D187

Subgroups

subgroupG/H
center, hypercenterC7D1683
commutator, cosocle, hypocenterC9×C11×C17C2×C7
FrattiniC3C7×D561
FittingC7×C9×C11×C17C2
socleC3×C7×C11×C17D3
LCSG ▷ C9×C11×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5901 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 13);