Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#72210469 (order 6144) · Inn(G) = C2×#67 · Out(G) = C22×#120 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #486 |
118 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)(6,10)(13,16)(14,19)(17,18);(4,6,7,10)(5,8,9,11);(2,3)(4,5)(6,8)(7,9)(10,11)(12,13,14,17,15,18,19,16)Polycyclic presentation:
2^6,3|a^2=e,b^2=d,e^2=f,c^a=cde,g^a=g^2,c^b=cd,e^c=ef36 conjugacy classes — view the full character table.
| maximal subgroup of | #68392, #68393, #68396, … |
| maximal normal subgroup of | #68392, #68393, #68396, … |
| maximal quotient of | #69571, #69574, #69582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 629);