Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of D48 |
| automorphism | Aut(G) = C2×D3×AGL(1,ℤ/16) (order 1536) · Inn(G) = D24 · Out(G) = C23×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #368 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,16,32,9,19,23,33,10,20,21,25,7,17,8,18)(5,11,22,29,12,26,28,31,14,27,35,34,24,30,13,15);(2,3)(4,5,7,12,10,14,9,24)(6,15,17,29,20,31,19,34)(8,22,21,28,23,35,16,13)(11,25,26,33,27,32,30,18)Polycyclic presentation:
2^6,3|a^2=c,b^2=de,c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^254 conjugacy classes — view the full character table.
| maximal subgroup of | #67579, #67581, #67593, … |
| maximal normal subgroup of | #67579, #67581, #67593, … |
| maximal quotient of | #67500, #67501, #67808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 65);