Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#511790 (order 6144) · Inn(G) = C22×D3 · Out(G) = C2×#2846 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #423 |
126 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)(9,12)(13,15);(4,5,6,7);(2,3)(5,7)(8,9,10,13,11,12,14,15)Polycyclic presentation:
2^6,3|a^2=d,b^2=e,d^2=f,b^a=be,c^a=cf,g^a=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #67620, #67631, #67669, … |
| maximal normal subgroup of | #67620, #67631, #67669, … |
| maximal quotient of | #69391, #69392, #69394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 483);