Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #4487 |
| automorphism | Aut(G) = D3×#3109 (order 768) · Inn(G) = #808 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #365 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6,7,12,10,15,9,5)(8,17,16,19,18,11,13,14);(2,3)(4,5,8,11,9,6,13,14,10,12,18,17,7,15,16,19)Polycyclic presentation:
2^6,3|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bde,c^a=cf,g^a=g^2,d^b=de,e^b=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #69254, #69257, #69264, … |
| maximal normal subgroup of | #69254, #69257, #69264, … |
| maximal quotient of | #67464, #67730, C2×#4494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 53);