Finite Group Databasebeta

← Prev (#72248996) Next (#72248998) →

C4×#4341⋊C5 #72248997

order3520
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC4×#4341⋊C5

Splittings

FittingC4×D4×C11 ⋊ C2×C5
HallC4×#4341 ⋊ C5
HallC11⋊C5 ⋊ C4×#41
SylowC11 ⋊ C4×C5×#41

Subgroups

subgroupG/H
centerC2×C4C22×AGL(1,𝔽11)
commutatorC2×C11C23×C4×C5
FrattiniC22C23×AGL(1,𝔽11)
FittingC4×D4×C11C2×C5
socle, cosocleC22×C11C24×C5
prime radicalC2×#4341⋊C5C2
hypercenterC4×D4AGL(1,𝔽11)
hypocenterC11C4×C5×#41
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×D4

620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#41×AGL(1,𝔽11), #72254515
maximal normal subgroup ofC4×#41×AGL(1,𝔽11), #72254515

GAP

Past the SmallGroups library coverage — no SmallGroups id.