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#97×AGL(1,𝔽11) #72248703

order3520
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23

Aliases

direct product#97×AGL(1,𝔽11)

Splittings

FittingC11×#97 ⋊ C2×C5
HallD11×#97 ⋊ C5
HallC11⋊C5 ⋊ C2×#97
SylowC11 ⋊ C2×C5×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×AGL(1,𝔽11)
commutatorC2×C11C2×C42×C5
FittingC11×#97C2×C5
socleC22×C11C22×C4×C5
prime radicalC22×AGL(1,𝔽11)C2×C4
cosocleC2×C4×C11C23×C5
hypercenter#97AGL(1,𝔽11)
hypocenterC11C2×C5×#97
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #97

292 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 148 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) = 352

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#442×AGL(1,𝔽11), #347×AGL(1,𝔽11), #444×AGL(1,𝔽11), …
maximal normal subgroup of#442×AGL(1,𝔽11), #347×AGL(1,𝔽11), #444×AGL(1,𝔽11), …
maximal quotient of#347×AGL(1,𝔽11), #322×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.