Finite Group Databasebeta

← Prev (#39911874) Next (#39911876) →

C3×C11⋊#11716322 #39911875

order26334
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊#11716322
unambiguous semidirect productC11⋊(C3×#11716322)

Splittings

Fitting, socleC3×C7×C11×C19 ⋊ C2×C3
derived, HallC7×C11×C19 ⋊ C2×C32
HallC3×C11×#87705 ⋊ C2
HallC7×D209 ⋊ C32
HallC3×#87705 ⋊ D11
HallD209 ⋊ C3×ΓL(1,𝔽8)
HallC11×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C32×D11
HallC7×C11 ⋊ C3×D19⋊C3
SylowC19 ⋊ C3×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C3×#11716322
SylowC7 ⋊ C3×C11⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#11716322
commutator, cosocle, hypocenterC7×C11×C19C2×C32
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2×C3
LCSG ▷ C7×C11×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 102);