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GL(2,ℤ/4)×AGL(1,𝔽13) #72242293

order14976
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productGL(2,ℤ/4)×AGL(1,𝔽13)

Splittings

FittingC24×C13 ⋊ C3×C4×D3
SylowC13 ⋊ C3×C4×GL(2,ℤ/4)

Subgroups

subgroupG/H
center, FrattiniC2C2×S4×AGL(1,𝔽13)
commutatorC2×A4×C13C22×C3×C4
FittingC24×C13C3×C4×D3
socleC23×C13C2×C3×C4×D3
prime radicalD13⋊C3×GL(2,ℤ/4)C2
cosocleC2×A4×D13C23×C3
hypercenterC22S4×AGL(1,𝔽13)
hypocenterA4×C13C3×C4×D4
LCSG ▷ C2×A4×C13 ▷ A4×C13
UCSC1 ◁ C2 ◁ C22

2096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 156

A minimal faithful permutation representation — 3 generators on 21 points:

(2,4)(5,7,8)(9,10,19)(11,13,15)(12,18,16)(14,21,17);(10,11,13,16)(12,15,18,14)(17,21,19,20);(1,2)(3,4)(6,7)

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽13)×A4⋊S4

GAP

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

gap> G := Group((2,4)(5,7,8)(9,10,19)(11,13,15)(12,18,16)(14,21,17), (10,11,13,16)(12,15,18,14)(17,21,19,20), (1,2)(3,4)(6,7));