Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#2196 (order 1536) · Inn(G) = #882 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#100 ⋊ C2 |
| 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)(4,6,7,14,8,13,16,19)(5,9,10,12,11,17,15,18);(6,13)(7,16)(10,15)(12,18);(2,3)(4,5)(6,12)(7,15)(8,11)(9,14)(10,16)(13,18)(17,19)Polycyclic presentation:
2^6,3|c^2=d,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^2,c^b=ce,d^b=df,e^c=ef27 conjugacy classes — view the full character table.
| maximal subgroup of | #69131, #69132, #69138, … |
| maximal normal subgroup of | #69131, #69132, #69138, … |
| maximal quotient of | #68108, #68109, #68110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 305);