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D5×C11×C3⋊AGL(1,𝔽7) #28357605

order13860
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×C3⋊AGL(1,𝔽7)
unambiguous semidirect product(C3×D5)⋊(C11×AGL(1,𝔽7))
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊(D3×C11)
unambiguous semidirect product(D5×D21)⋊(C3×C11)
unambiguous semidirect product(D5×C11×D21)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C22×C3
derivedC3×C5×C7 ⋊ C22×C3×C11
HallC3×C5×C11×ΓL(1,𝔽8) ⋊ C22
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×C7×C11 ⋊ C2×C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C22×C11
HallC7×C11 ⋊ C3×D3×D5
HallC3×ΓL(1,𝔽8) ⋊ C2×D5×C11
HallC5×C11 ⋊ C2×C3⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D3×C11
SylowC7 ⋊ C3×D3×D5×C11
SylowC5 ⋊ C2×C11×C3⋊AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC11D5×C3⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22×C3
LCSG ▷ C3×C5×C7
UCSC1 ◁ C11

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 272);