Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = D3×#2196 (order 768) · Inn(G) = #217 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #101 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6,8,14)(5,9,11,12)(7,15,16,13)(10,18,19,17);(2,3)(4,5,7,10,8,11,16,19)(6,12,13,18,14,9,15,17)Polycyclic presentation:
2^5,3|a^2=c,b^2=e,c^2=e,b^a=bd,d^a=de,f^a=f^2,c^b=ce21 conjugacy classes — view the full character table.
| maximal subgroup of | #4477, #4478, #4542, … |
| maximal normal subgroup of | #4477, #4478, #4542, … |
| maximal quotient of | #4528, #4530, #4543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 43);