Finite Group Databasebeta

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AGL(1,𝔽5)×Dic11⋊C5 #72276344

order4400
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C4

Aliases

direct productAGL(1,𝔽5)×Dic11⋊C5

Splittings

derivedC5×C11 ⋊ C42×C5
HallC5×C11⋊C5 ⋊ C42
SylowC11 ⋊ C4×C5×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2AGL(1,𝔽5)×AGL(1,𝔽11)
commutator, hypocenterC5×C11C42×C5
Fitting, socleC2×C5×C11C2×C4×C5
prime radicalC2×D5×C11⋊C5C22
cosocleC2×D5×C11C22×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2

126 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 46 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

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,𝔽5)×AGL(1,𝔽11), #72276384, AGL(1,𝔽5)×(C11⋊C5)⋊AGL(1,𝔽5), …
maximal normal subgroup ofC4×AGL(1,𝔽5)×AGL(1,𝔽11), AGL(1,𝔽5)×C22⋊AGL(1,𝔽11), #72276412
maximal quotient of#72276384, AGL(1,𝔽5)×(C11⋊C5)⋊AGL(1,𝔽5)

GAP

Past the SmallGroups library coverage — no SmallGroups id.