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C9×C4⋊AGL(1,𝔽7) #13094249

order1512
isoclinismisoclinic class of ΓL(1,𝔽8)⋊Q8
automorphism?
homologyAbelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3

Aliases

direct productC9×C4⋊AGL(1,𝔽7)
unambiguous semidirect productC4⋊(C9×AGL(1,𝔽7))

Splittings

FittingC4×C7×C9 ⋊ C2×C3
HallC9×ΓL(1,𝔽8) ⋊ D4
HallD28 ⋊ C3×C9
SylowC7 ⋊ C3×D4×C9

Subgroups

subgroupG/H
centerC2×C9C2×AGL(1,𝔽7)
commutatorC2×C7C22×C3×C9
FrattiniC2×C3C2×C3×AGL(1,𝔽7)
FittingC4×C7×C9C2×C3
socle, cosocleC2×C3×C7C22×C32
prime radicalC3×C4⋊AGL(1,𝔽7)C3
hypercenterC4×C9AGL(1,𝔽7)
hypocenterC7C3×D4×C9
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C9 ◁ C4×C9

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 252

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×C9×AGL(1,𝔽7), D9×C4⋊AGL(1,𝔽7), #72278028
maximal normal subgroup ofD4×C9×AGL(1,𝔽7), D9×C4⋊AGL(1,𝔽7), #72278028

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 146);