Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#3025 (order 768) · Inn(G) = #217 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #349 |
58 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)(5,9)(6,12)(11,16)(13,18);(2,3)(4,5,6,10,7,11,13,17,8,9,12,15,14,16,18,19)Polycyclic presentation:
2^6,3|a^2=c,c^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^2,c^b=cf42 conjugacy classes — view the full character table.
| maximal subgroup of | #67481, #67482, #67483, … |
| maximal normal subgroup of | #67481, #67482, #67483, … |
| maximal quotient of | #67664, #67673, #67709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 112);