Finite Group Databasebeta

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C11×D1071 #37555621

order23562
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1071
unambiguous semidirect productC7⋊(C11×D153)
unambiguous semidirect productC9⋊(C11×D119)
unambiguous semidirect productC17⋊(C11×D63)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC7×C9×C17 ⋊ C2×C11
HallC9×C11×C17 ⋊ D7
HallC7×C11×C17 ⋊ D9
HallC7×C9×C11 ⋊ D17
HallC11×C17 ⋊ D63
HallC9×C17 ⋊ C11×D7
HallC7×C17 ⋊ C11×D9
HallC9×C11 ⋊ D119
HallC7×C11 ⋊ D153
HallC7×C9 ⋊ C11×D17
SylowC17 ⋊ C11×D63
SylowC9 ⋊ C11×D119
SylowC7 ⋊ C11×D153

Subgroups

subgroupG/H
center, hypercenterC11D1071
commutator, cosocle, hypocenterC7×C9×C17C2×C11
FrattiniC3C11×D357
FittingC7×C9×C11×C17C2
socleC3×C7×C11×C17D3
LCSG ▷ C7×C9×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 15);