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C4×AGL(1,𝔽5)×D11 #13183304

order1760
isoclinismisoclinic class of AGL(1,𝔽5)×D11
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×AGL(1,𝔽5)×D11

Splittings

FittingC4×C5×C11 ⋊ C2×C4
derived, HallC5×C11 ⋊ C2×C42
SylowC11 ⋊ C2×C4×AGL(1,𝔽5)
SylowC5 ⋊ C42×D11

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,𝔽5)×D11
commutator, hypocenterC5×C11C2×C42
FrattiniC2C2×AGL(1,𝔽5)×D11
FittingC4×C5×C11C2×C4
socleC2×C5×C11C22×C4
prime radicalC2×D5×D11C22
cosocleC2×D5×C11C23
LCSG ▷ C5×C11
UCSC1 ◁ C4

216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 220

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×D11, AGL(1,𝔽5)2×D11, C4×AGL(1,𝔽5)×AGL(1,𝔽11)
maximal normal subgroup ofD4×AGL(1,𝔽5)×D11, C4×AGL(1,𝔽5)×AGL(1,𝔽11)
maximal quotient ofAGL(1,𝔽5)2×D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1113);