Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#3003 (order 768) · Inn(G) = D3×D4 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ #444 |
104 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)(4,7,8,11,10,15,9,19)(5,12,13,18,14,6,16,17);(4,6,9,18,10,12,8,17)(5,11,13,15,14,19,16,7);(2,3)(4,5)(6,15)(7,12)(8,13)(9,16)(10,14)(11,18)(17,19)Polycyclic presentation:
2^6,3|b^2=e,c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^2,c^b=ce,e^c=ef36 conjugacy classes — view the full character table.
| maximal subgroup of | #69254, #69264, #69309, … |
| maximal normal subgroup of | #69254, #69264, #69309, … |
| maximal quotient of | #68517, #68518, #68519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 453);