Finite Group Databasebeta

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C7×C11×D153 #37555617

order23562
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D153
unambiguous semidirect productC9⋊(C7×C11×D17)
unambiguous semidirect productC17⋊(C7×C11×D9)

Splittings

Fitting, HallC7×C9×C11×C17 ⋊ C2
derived, HallC9×C17 ⋊ C2×C7×C11
HallC9×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ D9
HallC7×C9×C17 ⋊ C2×C11
HallC7×C9×C11 ⋊ D17
HallC11×C17 ⋊ C7×D9
HallC7×C17 ⋊ C11×D9
HallC9×C11 ⋊ C7×D17
HallC7×C9 ⋊ C11×D17
SylowC17 ⋊ C7×C11×D9
SylowC9 ⋊ C7×C11×D17

Subgroups

subgroupG/H
center, hypercenterC7×C11D153
commutator, cosocle, hypocenterC9×C17C2×C7×C11
FrattiniC3C7×C11×D51
FittingC7×C9×C11×C17C2
socleC3×C7×C11×C17D3
LCSG ▷ C9×C17
UCSC1 ◁ C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 11);