Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#6628842 (order 3072) · Inn(G) = C2×D12 · Out(G) = C2×#120 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #441 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(4,5,6,7)(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)(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,c^2=d,e^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 | #69090, #70928, #78494, … |
| maximal normal subgroup of | #69090, #70928, #78494, … |
| maximal quotient of | #68084, #68087, #68089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 275);