Finite Group Databasebeta

#44501955

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

Aliases

No aliases for this group.

Splittings

FittingC3×C9×C379 ⋊ C3
SylowC379 ⋊ #737

Subgroups

subgroupG/H
centerC9C3×C379⋊C3
commutator, socle, cosocleC3×C379C33
FrattiniC3C32×C379⋊C3
FittingC3×C9×C379C3
prime radicalC32⋊(C379⋊C3)C3
hypercenterC3×C9C379⋊C3
hypocenterC379#737
LCSG ▷ C3×C379 ▷ C379
UCSC1 ◁ C9 ◁ C3×C9

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10233

Polycyclic presentation:

3^4,379|c^3=d,b^a=bd,e^b=e^327

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, 47);