Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C25×D3×D4 (order 1536) · Inn(G) = #67 · Out(G) = C26 |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #340 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(8,9,10,11)(13,16)(14,19)(17,18);(2,3)(4,5,6,7)(12,13,14,17,15,18,19,16)Polycyclic presentation:
2^6,3|a^2=d,b^2=c,d^2=f,b^a=bde,g^a=g^2,d^b=df48 conjugacy classes — view the full character table.
| maximal subgroup of | #68780, #68781, #68782, … |
| maximal normal subgroup of | #68780, #68781, #68782, … |
| maximal quotient of | #67612, #67619, #67620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 88);