Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #826 |
| automorphism | Aut(G) = D3×#442 (order 384) · Inn(G) = #213 · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×Q16 ⋊ C2 |
| Sylow | C3 ⋊ SD32 |
26 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)(4,5,8,11)(6,13,15,19)(7,16,14,10)(9,17,18,12);(2,3)(5,9)(6,12)(7,14)(10,19)(11,18)(13,16)(15,17)Polycyclic presentation:
2^5,3|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,c^b=cd,d^b=de18 conjugacy classes — view the full character table.
| maximal subgroup of | D3×SD32, #4914, #4918, … |
| maximal normal subgroup of | D3×SD32, #4914, #4918, … |
| maximal quotient of | #4490, #4491, #4564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 35);