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AGL(1,𝔽5)×C22⋊D11 #13183321

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

Aliases

direct productAGL(1,𝔽5)×C22⋊D11

Splittings

FittingC22×C5×C11 ⋊ C2×C4
HallC5×C11 ⋊ C4×D4
SylowC11 ⋊ D4×AGL(1,𝔽5)
SylowC5 ⋊ C4×C22⋊D11

Subgroups

subgroupG/H
center, FrattiniC2C2×AGL(1,𝔽5)×D11
commutator, socleC2×C5×C11C22×C4
FittingC22×C5×C11C2×C4
prime radicalD5×C22⋊D11C2
cosocleC2×D5×C11C23
hypercenterC22AGL(1,𝔽5)×D11
hypocenterC5×C11C4×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C22

188 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 54 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

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×C22⋊AGL(1,𝔽11)
maximal normal subgroup ofD4×AGL(1,𝔽5)×D11, AGL(1,𝔽5)×C22⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1130);