Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 12288 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #381 |
218 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)(4,5,6,7)(9,11)(14,18)(16,19);(12,14)(13,16)(15,18)(17,19);(2,3)(8,9)(10,11)(12,13,15,17)(14,16,18,19)Polycyclic presentation:
2^6,3|a^2=f,c^2=d,c^a=ce,g^a=g^2,c^b=cf48 conjugacy classes — view the full character table.
| maximal subgroup of | #67445, #68953, #68954, … |
| maximal normal subgroup of | #67445, #68953, #68954, … |
| maximal quotient of | #69402, #69422, #69423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 502);