Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C23×D3×#120 (order 1536) · Inn(G) = C2×D3 · Out(G) = C22×#120 |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #336 |
118 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)(9,11)(12,13,14,16,15,17,18,19);(2,3)(4,5,6,7)(8,9)(10,11)Polycyclic presentation:
2^6,3|a^2=c,b^2=d,d^2=f,b^a=be,g^a=g^272 conjugacy classes — view the full character table.
| maximal subgroup of | #68596, #68597, #68598, … |
| maximal normal subgroup of | #68596, #68597, #68598, … |
| maximal quotient of | C3⋊#1273, #67655, #67656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 109);