Finite Group DatabasebetaFinite Group Databasebeta| order | 1764 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×ΓL(1,𝔽8)2 |
| Fitting, socle, Hall | C22×C72 ⋊ C32 |
| derived, Sylow | C72 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | ΓL(1,𝔽8)2 |
| commutator, cosocle, hypocenter | C72 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72 | C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1764, 164);