Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C22×D3×D4 (order 192) · Inn(G) = #67 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #108 |
30 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)(4,6,7,15,9,16,8,17)(5,10,11,14,13,18,12,19);(2,3)(4,5,8,12,9,13,7,11)(6,14,15,18,16,19,17,10)Polycyclic presentation:
2^5,3|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,f^a=f^2,d^b=de24 conjugacy classes — view the full character table.
| maximal subgroup of | #4748, #4749, #4754, … |
| maximal normal subgroup of | #4748, #4749, #4754, … |
| maximal quotient of | #4479, #4480, #4558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 29);