Finite Group DatabasebetaFinite Group Databasebeta| order | 30366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C7×C241 ⋊ C2×C32 |
| Hall | ΓL(1,𝔽8)×C241⋊C3 ⋊ C2 |
| Hall | D1687 ⋊ C32 |
| Sylow | C241 ⋊ C3×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C3×D241⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C241 | C2×C32 |
| LCS | G ▷ C7×C241 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1687 |
Polycyclic presentation:
2,3^2,7,241|d^a=d^6,e^a=e^240,e^b=e^225,d^c=d^2221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30366, 26);