Finite Group DatabasebetaFinite Group Databasebeta| order | 30699 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | C379 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #16811789 |
| commutator, hypocenter | C379 | C3×C27 |
| Frattini | C3 | C3×#16811789 |
| Fitting | C9×C379 | C9 |
| socle | C3×C379 | C3×C9 |
| prime radical | C3×C379⋊C3 | C9 |
| cosocle | #16811787 | C32 |
| LCS | G ▷ C379 | |
| UCS | C1 ◁ C9 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10233 |
Polycyclic presentation:
3^4,379|a^3=c,c^3=d,e^a=e^180,e^b=e^51,e^c=e^327459 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30699, 56);