Finite Group Databasebeta

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C22×C5×AGL(1,𝔽11) #72276312

order2200
automorphism?
homologyAbelianization (H1) = C23×C52 · Schur multiplier (H2) = C23×C5

Aliases

direct productC22×C5×AGL(1,𝔽11)

Splittings

Fitting, socleC22×C5×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C23×C52
HallC5×C11⋊C5 ⋊ C23
HallC22×D11 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC22×C5AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C23×C52
FrattiniC1G
Fitting, socleC22×C5×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C22×C5

256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D5×AGL(1,𝔽11), C5×D4×AGL(1,𝔽11), C22⋊D5×AGL(1,𝔽11), …
maximal normal subgroup ofC22×D5×AGL(1,𝔽11), C5×D4×AGL(1,𝔽11), C22⋊D5×AGL(1,𝔽11), …
maximal quotient ofC5×D4×AGL(1,𝔽11), C22×(C11⋊C5)⋊AGL(1,𝔽11), C2×AGL(1,𝔽11)2

GAP

Past the SmallGroups library coverage — no SmallGroups id.