Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#612424 (order 3072) · Inn(G) = C2×D12 · Out(G) = C2×#120 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #480 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(5,9)(6,11)(12,13,17,19,15,18,14,16);(4,6)(5,8)(7,11)(9,10);(2,3)(4,5)(6,10)(7,9)(8,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^6,3|c^2=def,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,c^b=ce39 conjugacy classes — view the full character table.
| maximal subgroup of | #68110, #68111, #68134, … |
| maximal normal subgroup of | #68110, #68111, #68134, … |
| maximal quotient of | #68621, #68625, #68635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 295);