Finite Group Databasebeta

← Prev (#72276347) Next (#72276349) →

C4×C5×AGL(1,𝔽11) #72276348

order2200
automorphism?
homologyAbelianization (H1) = C2×C4×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC4×C5×AGL(1,𝔽11)

Splittings

FittingC4×C5×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C4×C52
HallC5×C11⋊C5 ⋊ C2×C4
HallC4×D11 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC4×C5AGL(1,𝔽11)
commutator, hypocenterC11C2×C4×C52
FrattiniC2C2×C5×AGL(1,𝔽11)
FittingC4×C5×C11C2×C5
socleC2×C5×C11C22×C5
prime radicalC2×C5×AGL(1,𝔽11)C2
cosocleC2×C11C22×C52
LCSG ▷ C11
UCSC1 ◁ C4×C5

128 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 ofC4×D5×AGL(1,𝔽11), C5×D4×AGL(1,𝔽11), D20×AGL(1,𝔽11), …
maximal normal subgroup ofC4×D5×AGL(1,𝔽11), C5×D4×AGL(1,𝔽11), D20×AGL(1,𝔽11)
maximal quotient ofC5×AGL(1,𝔽5)×AGL(1,𝔽11), #72276523, C4×(C11⋊C5)⋊AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.