Finite Group Databasebeta

C3×#23779521 #44501952

order30699
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#23779521

Splittings

FittingC3×C9×C379 ⋊ C3
SylowC379 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C379⋊C3
commutator, cosocleC3×C379C33
FrattiniC3C32×C379⋊C3
FittingC3×C9×C379C3
socleC32×C379C32
prime radicalC32×C379⋊C3C3
hypercenterC3×C9C379⋊C3
hypocenterC379C3×3−1+2
LCSG ▷ C3×C379 ▷ C379
UCSC1 ◁ C32 ◁ C3×C9

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10233

Conjugacy classes & character table

3435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30699, 44);