Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#2196 (order 1536) · Inn(G) = #953 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #455 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(7,17)(10,15)(12,19)(14,16);(4,6)(5,9)(7,16)(8,13)(10,19)(11,18)(12,15)(14,17);(2,3)(4,5,8,11)(6,12,13,19)(7,15,17,10)(9,16,18,14)Polycyclic presentation:
2^6,3|a^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^2,d^b=df,e^b=ef,e^c=ef33 conjugacy classes — view the full character table.
| maximal subgroup of | #70997, #70998, #71000, … |
| maximal normal subgroup of | #70997, #70998, #71000, … |
| maximal quotient of | #71647, #71649, #71665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 801);