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C4×C5⋊AGL(1,𝔽11) #72276351

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

Aliases

direct productC4×C5⋊AGL(1,𝔽11)

Splittings

FittingC4×C5×C11 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C4×C5
HallC5×C11⋊C5 ⋊ C2×C4
SylowC11 ⋊ C4×C5×D5

Subgroups

subgroupG/H
center, hypercenterC4C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C2×C4×C5
FrattiniC2C2×C5⋊AGL(1,𝔽11)
FittingC4×C5×C11C2×C5
socle, cosocleC2×C5×C11C22×C5
prime radicalC2×C5⋊AGL(1,𝔽11)C2
LCSG ▷ C5×C11
UCSC1 ◁ C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D5×AGL(1,𝔽11), D4×C5⋊AGL(1,𝔽11), AGL(1,𝔽5)×C5⋊AGL(1,𝔽11), …
maximal normal subgroup ofC4×D5×AGL(1,𝔽11), D4×C5⋊AGL(1,𝔽11), #72276389
maximal quotient ofAGL(1,𝔽5)×C5⋊AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.