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C4⋊C4×AGL(1,𝔽11) #13182493

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C4⋊C4)
unambiguous semidirect product(C4⋊C4×D11)⋊C5

Splittings

FittingC11×C4⋊C4 ⋊ C2×C5
HallC4⋊C4×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C4⋊C4
SylowC11 ⋊ C2×C5×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×AGL(1,𝔽11)
commutatorC2×C11C22×C4×C5
FittingC11×C4⋊C4C2×C5
socle, cosocleC22×C11C23×C5
prime radicalC22×AGL(1,𝔽11)C22
hypercenterC4⋊C4AGL(1,𝔽11)
hypocenterC11C2×C5×C4⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4⋊C4

184 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 176

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#106×AGL(1,𝔽11), C4×D4×AGL(1,𝔽11), #102×AGL(1,𝔽11), …
maximal normal subgroup of#106×AGL(1,𝔽11), C4×D4×AGL(1,𝔽11), #102×AGL(1,𝔽11), …
maximal quotient of#106×AGL(1,𝔽11), #108×AGL(1,𝔽11), #72269648, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 302);