Finite Group Databasebeta

← Prev (#72276490) Next (#72276492) →

C4×A4×C11⋊C5 #72276491

order2640
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC4×A4×C11⋊C5

Splittings

Fitting, HallC22×C4×C11 ⋊ C3×C5
derivedC22×C11 ⋊ C3×C4×C5
HallC22×C4×C11⋊C5 ⋊ C3
HallC4×C11×A4 ⋊ C5
SylowC22×C4 ⋊ C3×C11⋊C5
SylowC11 ⋊ C4×C5×A4

Subgroups

subgroupG/H
center, hypercenterC4A4×C11⋊C5
commutator, hypocenterC22×C11C3×C4×C5
FrattiniC2C2×A4×C11⋊C5
FittingC22×C4×C11C3×C5
socle, cosocleC23×C11C2×C3×C5
prime radicalC2×A4×C11⋊C5C2
LCSG ▷ C22×C11
UCSC1 ◁ C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 19 points:

(2,3,4)(5,6,7,8)(10,11,13,16,14)(12,15,18,17,19);(1,4)(2,3)(9,10,12,11,14,16,15,18,19,13,17)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×AGL(1,𝔽5)×C11⋊C5
maximal quotient ofA4×AGL(1,𝔽5)×C11⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,3,4)(5,6,7,8)(10,11,13,16,14)(12,15,18,17,19), (1,4)(2,3)(9,10,12,11,14,16,15,18,19,13,17));