Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#72210469 (order 6144) · Inn(G) = C2×#67 · Out(G) = C22×#120 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #487 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,11)(5,9,8,10)(13,16)(14,19)(17,18);(4,5,7,8)(6,10,11,9);(2,3)(5,8)(9,10)(12,13,15,18)(14,16,19,17)Polycyclic presentation:
2^6,3|a^2=f,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,c^b=ce,d^c=df36 conjugacy classes — view the full character table.
| maximal subgroup of | #68434, #68435, #68445, … |
| maximal normal subgroup of | #68434, #68435, #68445, … |
| maximal quotient of | #69574, #69579, #69589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 652);