Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#6628842 (order 3072) · Inn(G) = C2×D12 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #470 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7)(10,18)(13,22)(16,23)(19,21);(8,10,17,21,12,18,11,19)(9,13,20,23,15,22,14,16);(2,3)(4,5)(6,7)(8,9,12,15)(10,16,18,23)(11,20,17,14)(13,21,22,19)Polycyclic presentation:
2^6,3|a^2=f,b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^2,c^b=cf36 conjugacy classes — view the full character table.
| maximal subgroup of | #67482, #67484, #67536, … |
| maximal normal subgroup of | #67482, #67484, #67536, … |
| maximal quotient of | #69817, #69820, #69824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 696);