Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = D3×D42 (order 384) · Inn(G) = (C2×D3)⋊C4 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ #100 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 11 points:
(1,2,3)(4,5,6,9,7,8,10,11);(2,3)(5,8)(6,10)Polycyclic presentation:
2^5,3|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^2,d^b=de21 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#100, #4749, #4751, … |
| maximal normal subgroup of | D3×#100, #4749, #4751, … |
| maximal quotient of | #4464, #4468, #4481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 30);