Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C23×D3×#120 (order 1536) · Inn(G) = C22×D3 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #432 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(6,10)(8,11)(12,13,14,17,15,16,18,19);(4,6)(5,8)(7,10)(9,11);(2,3)(4,5,7,9)(6,8,10,11)(13,16)(17,19)Polycyclic presentation:
2^6,3|a^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^2,c^b=ce48 conjugacy classes — view the full character table.
| maximal subgroup of | #68102, #68103, #68104, … |
| maximal normal subgroup of | #68102, #68103, #68104, … |
| maximal quotient of | #68597, #68603, #68605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 278);