Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = D3×#15947 (order 1536) · Inn(G) = C2×D3 · Out(G) = #2403 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic3⋊C4 |
| Sylow | C3 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 13 points:
(3,4,5)(7,9)(10,11,12,13);(4,5)(6,7,8,9);(1,2)36 conjugacy classes — view the full character table.
| maximal subgroup of | #4469, #4646, #4647, … |
| maximal normal subgroup of | #4469, #4646, #4647, … |
| maximal quotient of | #4928, C4×Dic3⋊C4, #4942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 130);