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(C2×AGL(1,𝔽13))⋊C4 #11928186

order1248
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C23

Aliases

unambiguous semidirect product(C2×AGL(1,𝔽13))⋊C4
unambiguous semidirect product((C2×#261)⋊C4)⋊C3

Splittings

FittingC2×C4×C13 ⋊ C3×C4
Hall(C2×#261)⋊C4 ⋊ C3
HallC13⋊C3 ⋊ #95
SylowC13 ⋊ C3×#95

Subgroups

subgroupG/H
center, FrattiniC22C2×AGL(1,𝔽13)
commutatorC2×C13C3×C42
FittingC2×C4×C13C3×C4
socleC22×C13C2×C3×C4
prime radicalC22×D13⋊C3C22
cosocleC22×D13C22×C3
hypercenterC2×C4AGL(1,𝔽13)
hypocenterC13C3×#95
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Polycyclic presentation:

2^2,3,2^3,13|a^2=d,b^2=e,b^a=bf,g^a=g^8,g^c=g^3,g^d=g^12

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22⋊C4×AGL(1,𝔽13), #72229007, #72229010, …
maximal normal subgroup ofC22⋊C4×AGL(1,𝔽13), #72229007, #72229010, …
maximal quotient of#72229042, #72229112, #72229120, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 298);