Finite Group Databasebeta

← Prev (#72216698) Next (#72216700) →

C23×C3⋊AGL(1,𝔽11) #72216699

order2640
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC23×C3⋊AGL(1,𝔽11)

Splittings

Fitting, socleC23×C3×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C24×C5
HallC23×D33 ⋊ C5
HallC3×C11⋊C5 ⋊ C24
HallC11⋊C5 ⋊ C23×D3
SylowC11 ⋊ C23×C5×D3
SylowC3 ⋊ C23×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC23C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C24×C5
FrattiniC1G
Fitting, socleC23×C3×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C23

536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×D3×AGL(1,𝔽11), C2×D4×C3⋊AGL(1,𝔽11), C2×#72216761, …
maximal normal subgroup ofC23×D3×AGL(1,𝔽11), C2×D4×C3⋊AGL(1,𝔽11), C2×#72216761, …
maximal quotient ofC2×D4×C3⋊AGL(1,𝔽11), #41×C3⋊AGL(1,𝔽11), C24×C3⋊AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.