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C3×#22552467 #38736603

order25029
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

direct productC3×#22552467

Splittings

FittingC3×H(3,𝔽3)×C103 ⋊ C3
SylowC103 ⋊ C3×#732

Subgroups

subgroupG/H
centerC32C32⋊(C103⋊C3)
commutator, cosocleC32×C103C33
FrattiniC32C32×C103⋊C3
FittingC3×H(3,𝔽3)×C103C3
socleC32×C103H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C103⋊C3
hypocenterC103C3×#732
LCSG ▷ C32×C103 ▷ C3×C103 ▷ C103
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8343

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25029, 252);