Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic14 |
| Hall | C7×Dic14 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ Q8 |
| Sylow | C72 ⋊ C3×Q8 |
51 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | #72244998, ΓL(1,𝔽8)×#1157, #72245007, … |
| maximal normal subgroup of | #72244998, ΓL(1,𝔽8)×#1157, #72245007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 108);