Finite Group Databasebeta

← Prev (#37555663) Next (#37555665) →

C7×C11×C3⋊D51 #37555664

order23562
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC7×C11×C3⋊D51
unambiguous semidirect productC3⋊(C7×C11×D51)
unambiguous semidirect productC17⋊(C7×C11×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, HallC32×C17 ⋊ C2×C7×C11
HallC32×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C3⋊D3
HallC32×C7×C17 ⋊ C2×C11
HallC32×C7×C11 ⋊ D17
HallC11×C17 ⋊ C7×C3⋊D3
HallC7×C17 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ C7×D17
HallC32×C7 ⋊ C11×D17
SylowC17 ⋊ C7×C11×C3⋊D3
SylowC32 ⋊ C7×C11×D17

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊D51
commutator, cosocle, hypocenterC32×C17C2×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C32×C17
UCSC1 ◁ C7×C11

96 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, 58);