Finite Group DatabasebetaFinite Group Databasebeta| order | 30303 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13×C37 ⋊ C32 |
| Hall | C13×C37 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C37 ⋊ C3×C13⋊C3 |
| Hall | C7×C13 ⋊ C3×C37⋊C3 |
| Sylow | C37 ⋊ ΓL(1,𝔽8)×C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C37⋊C3 |
| Sylow | C7 ⋊ C13⋊C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C37 | C32 |
| LCS | G ▷ C7×C13×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3367 |
Polycyclic presentation:
3^2,7,13,37|d^a=d^9,e^a=e^10,c^b=c^2,d^b=d^3431 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30303, 35);