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C7×C3⋊(C11⋊AGL(1,𝔽13)) #49114682

order36036
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C11⋊AGL(1,𝔽13))
unambiguous semidirect productC3⋊(C7×C11⋊AGL(1,𝔽13))
unambiguous semidirect productC11⋊(C7×C3⋊AGL(1,𝔽13))
unambiguous semidirect product(C3⋊(C11⋊#261))⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3×C4
derivedC3×C11×C13 ⋊ C3×C4×C7
HallC3×C7×C11×C13⋊C3 ⋊ C4
HallC3×C11×C13⋊C3 ⋊ C4×C7
HallC7×C11×C13 ⋊ C3×Dic3
HallC3×C7×C13⋊C3 ⋊ Dic11
HallC11×C13 ⋊ C3×C7×Dic3
HallC3×C13⋊C3 ⋊ C7×Dic11
HallC7×C13 ⋊ C3×Dic33
HallC7×C11 ⋊ C3⋊AGL(1,𝔽13)
SylowC13 ⋊ C3×C7×Dic33
SylowC11 ⋊ C7×C3⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊AGL(1,𝔽13))
commutator, hypocenterC3×C11×C13C3×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3×C4
prime radicalC3×C7×C11×D13⋊C3C2
cosocleC3×C11×D13C2×C3×C7
LCSG ▷ C3×C11×C13
UCSC1 ◁ C7

112 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 3003

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 350);