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C7×D15×AGL(1,𝔽11) #37528448

order23100
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D15×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C7×D15)
unambiguous semidirect product(C3×AGL(1,𝔽11))⋊(C7×D5)
unambiguous semidirect product(C5×AGL(1,𝔽11))⋊(D3×C7)
unambiguous semidirect product(D11×D15)⋊(C5×C7)
unambiguous semidirect product(C7×D11×D15)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C22×C5
derivedC3×C5×C11 ⋊ C22×C5×C7
HallC3×C5×C7×C11⋊C5 ⋊ C22
HallC5×C7×C11⋊C5 ⋊ C2×D3
HallC3×C5×C11⋊C5 ⋊ C22×C7
HallC5×C11⋊C5 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C2×C5×D5
HallC7×C11 ⋊ C2×C5×D15
HallC3×C11 ⋊ C2×C5×C7×D5
HallC3×C7 ⋊ D5×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C7×D15
SylowC3 ⋊ C7×D5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC7D15×AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C5×C11C22×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C7

192 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 54 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 259);