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C2×C11×C22⋊AGL(1,𝔽5) #13183343

order1760
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24

Aliases

direct productC2×C11×C22⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C11×C22⋊C4)
unambiguous semidirect product(C2×AGL(1,𝔽5))⋊(C22×C11)

Splittings

FittingC23×C5×C11 ⋊ C4
HallC5×C11 ⋊ C2×C22⋊C4
SylowC5 ⋊ C2×C11×C22⋊C4

Subgroups

subgroupG/H
centerC22×C11C2×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C11
FrattiniC2C22×C11×AGL(1,𝔽5)
FittingC23×C5×C11C4
socleC22×C5×C11C2×C4
prime radicalC23×D5×C11C2
cosocleC2×D5C23×C11
hypercenterC23×C11AGL(1,𝔽5)
hypocenterC5C2×C11×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C23×C11

264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 440

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1152);