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#13094147

order1512
automorphism?
homologyAbelianization (H1) = C32×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Hall#4427 ⋊ C8
HallC7⋊C8 ⋊ 3−1+2
SylowC7 ⋊ C8×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3×C4C3×AGL(1,𝔽7)
commutatorC3×C7C32×C8
FittingC4×C7×C9C2×C3
socleC2×C3×C7C32×C4
prime radicalC2×C3×ΓL(1,𝔽8)C3×C4
cosocleC3×C4×C7C2×C32
hypercenterC4×C9AGL(1,𝔽7)
hypocenterC7C8×3−1+2
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C3×C4 ◁ C4×C9

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 504

Polycyclic presentation:

2,3^2,2,3,2,7|a^2=d,c^3=e,d^2=f,g^a=g^6,c^b=ce,g^b=g^2

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 44);