Finite Group Databasebeta

← Prev (#39907634) Next (#39907636) →

C3×C79×AGL(1,𝔽11) #39907635

order26070
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C79 · Schur multiplier (H2) = C1

Aliases

direct productC3×C79×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×C79)
unambiguous semidirect product(C11⋊C5)⋊(C2×C3×C79)
unambiguous semidirect product(C3×D11)⋊(C5×C79)
unambiguous semidirect product(C3×D11×C79)⋊C5

Splittings

Fitting, socle, HallC3×C11×C79 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C3×C5×C79
HallC3×C11⋊C5×C79 ⋊ C2
HallC3×D11×C79 ⋊ C5
HallC11⋊C5×C79 ⋊ C2×C3
HallD11×C79 ⋊ C3×C5
HallC11×C79 ⋊ C2×C3×C5
HallC3×C11⋊C5 ⋊ C2×C79
HallC3×D11 ⋊ C5×C79
HallC11⋊C5 ⋊ C2×C3×C79
HallC3×C11 ⋊ C2×C5×C79
HallD11 ⋊ C3×C5×C79

Subgroups

subgroupG/H
center, hypercenterC3×C79AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C3×C5×C79
FrattiniC1G
Fitting, socleC3×C11×C79C2×C5
LCSG ▷ C11
UCSC1 ◁ C3×C79

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2607

Conjugacy classes & character table

2607 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26070, 21);