Finite Group Databasebeta

← Prev (#49114854) Next (#49114856) →

C2×C13×C3⋊(C11⋊AGL(1,𝔽7)) #49114855

order36036
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×C3⋊(C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C3)⋊(C13×C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C11)⋊(C13×C3⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C13×D33)
unambiguous semidirect product(C2×D231)⋊(C3×C13)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2×C3
derivedC3×C7×C11 ⋊ C22×C3×C13
HallC3×C11×C13×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×C13 ⋊ C2×C3×D3
HallC3×C13×ΓL(1,𝔽8) ⋊ C2×D11
HallC3×C11×ΓL(1,𝔽8) ⋊ C22×C13
HallC11×C13 ⋊ C2×C3⋊AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C3×D33
HallC7×C11 ⋊ C2×C3×D3×C13
HallC3×ΓL(1,𝔽8) ⋊ C2×C13×D11
SylowC11 ⋊ C2×C13×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C13×D33

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(C11⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC3×C7×C11C22×C3×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C13

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

2262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 523);