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C7×#4428 #13050509

order1323
isoclinismisoclinic class of #4427
automorphism?
homologyAbelianization (H1) = C32×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#4428

Splittings

FittingC72×C9 ⋊ C3
SylowC72 ⋊ 3−1+2

Subgroups

subgroupG/H
centerC3×C7C3×ΓL(1,𝔽8)
commutator, cosocleC3×C7C32×C7
FrattiniC3C3×C7×ΓL(1,𝔽8)
FittingC72×C9C3
socleC3×C72C32
prime radicalC3×C7×ΓL(1,𝔽8)C3
hypercenterC7×C9ΓL(1,𝔽8)
hypocenterC7C7×3−1+2
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C3×C7 ◁ C7×C9

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 189

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1323, 29);