Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = C2×D3×#3484 (order 1536) · Inn(G) = D12 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #339 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(9,12,13,14);(2,3)(4,5,6,7)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^6,3|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,e^a=ef,g^a=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #68645, #68646, #68694, … |
| maximal normal subgroup of | #68645, #68646, #68694, … |
| maximal quotient of | #67611, #67612, #67615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 82);