Finite Group Databasebeta

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C3×#21463360 #37555939

order23571
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#21463360

Splittings

FittingC3×3−1+2×C97 ⋊ C3
SylowC97 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C32⋊(C97⋊C3)
commutator, cosocleC32×C97C33
FrattiniC32C32×C97⋊C3
FittingC3×3−1+2×C97C3
socleC32×C97H(3,𝔽3)
hypercenterC3×3−1+2C97⋊C3
hypocenterC97C3×AΣL(1,𝔽27)
LCSG ▷ C32×C97 ▷ C3×C97 ▷ C97
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2619

Conjugacy classes & character table

1107 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23571, 246);