Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#63011 (order 1536) · Inn(G) = #217 · Out(G) = C25 |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #344 |
90 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)(4,6,7,14,8,13,15,19)(5,9,10,16,11,12,17,18);(2,3)(4,5)(6,12,13,9)(7,10)(8,11)(14,18,19,16)(15,17)Polycyclic presentation:
2^6,3|a^2=c,b^2=d,d^2=f,b^a=be,e^a=ef,g^a=g^2,c^b=cf42 conjugacy classes — view the full character table.
| maximal subgroup of | #68704, #68707, #68725, … |
| maximal normal subgroup of | #68704, #68707, #68725, … |
| maximal quotient of | #67661, #67666, #67670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 115);