Finite Group DatabasebetaFinite Group Databasebeta| order | 32298 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C769 ⋊ C2×C3 |
| Hall | #30633361 ⋊ C2 |
| Hall | C7×D769 ⋊ C3 |
| Hall | D769 ⋊ ΓL(1,𝔽8) |
| Sylow | C769 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D769⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C769 | C2×C3 |
| LCS | G ▷ C7×C769 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5383 |
Polycyclic presentation:
2,3,7,769|d^a=d^768,c^b=c^2,d^b=d^408906 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32298, 16);