Finite Group Databasebeta

C3×#22582680 #41008258

order26973
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC3×#22582680

Splittings

SylowC37 ⋊ C3×3−1+4

Subgroups

subgroupG/H
centerC32C33×C37⋊C3
commutator, cosocleC3×C37C35
FrattiniC3C34×C37⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C37C3
socleC32×C37C34
hypercenterC32×H(3,𝔽3)C37⋊C3
hypocenterC37C3×3−1+4
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C32×H(3,𝔽3)

5588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

1437 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4029);