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C2×(C11⋊C5)⋊(D7⋊C9) #28357372

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C11⋊C5)⋊(D7⋊C9)
unambiguous semidirect product(C2×C11⋊C5)⋊(D7⋊C9)
unambiguous semidirect product(C2×C7⋊C9)⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C7⋊AGL(1,𝔽11))⋊C9
unambiguous semidirect product(C2×C11⋊(D7⋊C9))⋊C5

Splittings

derived, HallC7×C11 ⋊ C22×C5×C9
HallC11⋊C5×C7⋊C9 ⋊ C22
HallC2×C11⋊(D7⋊C9) ⋊ C5
HallC2×C7⋊AGL(1,𝔽11) ⋊ C9
HallC11×C7⋊C9 ⋊ C22×C5
HallC7×C11⋊C5 ⋊ C22×C9
HallC2×D77 ⋊ C5×C9
HallC7⋊C9 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D7⋊C9
SylowC11 ⋊ C2×C5×D7⋊C9
SylowC7 ⋊ C2×C9×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C22×C5×C9
FrattiniC3C2×ΓL(1,𝔽8)⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×C7⋊AGL(1,𝔽11)C3
cosocleC3×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 1386

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 39);