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C3×#13133554 #19103167

order5103
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC3×#13133554

Splittings

SylowC7 ⋊ C3×#6893

Subgroups

subgroupG/H
centerC33C32×ΓL(1,𝔽8)
commutatorC32×C7C34
FrattiniC32C33×ΓL(1,𝔽8)
FittingC32×C7×H(3,𝔽3)C3
socleC33×C7C33
hypercenterC32×H(3,𝔽3)ΓL(1,𝔽8)
hypocenterC7C3×#6893
LCSG ▷ C32×C7 ▷ C7
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

1232 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

351 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5103, 3318);