Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C22×D3×#3003 (order 3072) · Inn(G) = C2×D12 · Out(G) = C26 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ #466 |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(5,7);(8,9,13,15,11,14,10,12);(2,3)(4,5)(6,7)(9,12)(10,13)(14,15)Polycyclic presentation:
2^6,3|b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^254 conjugacy classes — view the full character table.
| maximal subgroup of | #67485, #67487, #67526, … |
| maximal normal subgroup of | #67485, #67487, #67526, … |
| maximal quotient of | #69768, #69770, #69776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 674);