Finite Group DatabasebetaFinite Group Databasebeta| order | 30009 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C1429 ⋊ C3 |
| Sylow | C1429 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C1429⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C1429 | C3 |
| LCS | G ▷ C7×C1429 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10003 |
Polycyclic presentation:
3,7,1429|b^a=b^2,c^a=c^6643337 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30009, 5);