Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = D3×#23900 (order 1536) · Inn(G) = C2×D3 · Out(G) = #2403 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #117 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(9,13)(12,15);(8,10,11,14)(9,12,13,15);(2,3)(4,5,6,7)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^5,3|a^2=d,b^2=e,c^a=ce,f^a=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | #4523, #4531, #4555, … |
| maximal normal subgroup of | #4523, #4531, #4555, … |
| maximal quotient of | #4925, #4926, #4932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 133);