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C3×D5×C7⋊AGL(1,𝔽11) #37528435

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(D5×C11⋊C5)⋊(C3×D7)
unambiguous semidirect product(C3×D5×D77)⋊C5

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C22×C5
derivedC5×C7×C11 ⋊ C22×C3×C5
HallC3×C5×C7×C11⋊C5 ⋊ C22
HallC5×C7×C11⋊C5 ⋊ C22×C3
HallC3×C5×C11⋊C5 ⋊ C2×D7
HallC5×C11⋊C5 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C2×C5×D5
HallC7×C11 ⋊ C2×C3×C5×D5
HallC3×C11 ⋊ C5×D5×D7
HallC3×C7 ⋊ D5×AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D5×D7
SylowC7 ⋊ C3×D5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3D5×C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11C22×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3

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

normal subgroups only

This group has 192 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 246);