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#88100⋊C3 #11928172

order1248
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#88100⋊C3

Splittings

FittingC8×C13 ⋊ C3×C4
Hall#88100 ⋊ C3
HallC13⋊C3 ⋊ #97
SylowC13 ⋊ C3×#97

Subgroups

subgroupG/H
center, FrattiniC4C2×AGL(1,𝔽13)
commutator, socleC2×C13C3×C42
FittingC8×C13C3×C4
prime radicalC2×D13⋊C3C2×C4
cosocleC4×D13C22×C3
hypercenterC8AGL(1,𝔽13)
hypocenterC13C3×#97
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C8

80 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,e^2=f,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 ofM16×AGL(1,𝔽13), #72229200, #72229208, …
maximal normal subgroup ofM16×AGL(1,𝔽13), #72229200, #72229208, …
maximal quotient of#72229284, #72259297, C2×#88100⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 284);