Finite Group Databasebeta

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C2×C3×C11⋊#10587720 #49114829

order36036
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11⋊#10587720
unambiguous semidirect product(C2×C11)⋊(C3×#10587720)

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11×C13 ⋊ C22×C32
HallC3×C11×#63270 ⋊ C22
HallC2×C13×D77 ⋊ C32
HallC3×#63270 ⋊ C2×D11
HallC2×D77 ⋊ C3×C13⋊C3
HallC11×C13 ⋊ C2×C3×AGL(1,𝔽7)
HallC7×C13 ⋊ C2×C32×D11
HallC7×C11 ⋊ C22×C3×C13⋊C3
SylowC13 ⋊ C2×C3×C11⋊AGL(1,𝔽7)
SylowC11 ⋊ C2×C3×#10587720
SylowC7 ⋊ C2×C3×D11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊#10587720
commutator, cosocle, hypocenterC7×C11×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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

1152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 497);