Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = D3×#72214076 (order 6144) · Inn(G) = D12 · Out(G) = C2×#2403 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #427 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,11,12,19,13,20,10,17)(9,15,14,18,16,22,21,23);(8,10,13,12)(9,14,16,21)(11,17,20,19)(15,18,22,23);(2,3)(4,5,6,7)(8,9)(10,14)(11,18)(12,21)(13,16)(15,19)(17,22)(20,23)Polycyclic presentation:
2^6,3|a^2=d,b^2=f,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #67721, #67725, #67729, … |
| maximal normal subgroup of | #67721, #67725, #67729, … |
| maximal quotient of | #69729, #69732, C4×#817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 665);