Finite Group DatabasebetaFinite Group Databasebeta| order | 16212 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#11715871 |
| Fitting, socle, derived, Hall | C7×C193 ⋊ C3×C4 |
| Hall | C7⋊#11715871 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C193 ⋊ C4 |
| Sylow | C193 ⋊ ΓL(1,𝔽8)⋊C4 |
| Hall | ΓL(1,𝔽8) ⋊ #11715871 |
| Sylow | C7 ⋊ C3×#11715871 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C193 | C3×C4 |
| prime radical | ΓL(1,𝔽8)×D193 | C2 |
| cosocle | C7×D193 | C2×C3 |
| LCS | G ▷ C7×C193 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1351 |
Polycyclic presentation:
2,3,2,7,193|a^2=c,d^a=d^6,e^a=e^81,d^b=d^2,e^c=e^192254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16212, 31);