Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#63011 (order 1536) · Inn(G) = (C2×D3)⋊C4 · 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)(5,9,11,12)(7,13)(8,14)(10,17,18,19)(15,16);(2,3)(4,5,7,10,8,11,15,18)(6,12,13,19,14,9,16,17)Polycyclic presentation:
2^6,3|a^2=c,b^2=d,c^2=f,b^a=be,d^a=df,g^a=g^2,e^b=ef42 conjugacy classes — view the full character table.
| maximal subgroup of | #68696, #68699, #68700, … |
| maximal normal subgroup of | #68696, #68699, #68700, … |
| maximal quotient of | #67615, #67617, #67620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 92);