Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C26×D3 (order 384) · Inn(G) = C2×D3 · Out(G) = C25 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#67 |
| Fitting | C22×C3×C4 ⋊ C2 |
| Sylow | C3 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 11 points:
(1,2,3)(9,11);(2,3)(8,9)(10,11);(4,5,6,7)36 conjugacy classes — view the full character table.
| maximal subgroup of | #67⋊C8, #4728, #4729, … |
| maximal normal subgroup of | #67⋊C8, #4728, #4729, … |
| maximal quotient of | C4×Dic3⋊C4, #4933, C4×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 135);