Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C3×#376 ⋊ C2 |
| Sylow | C3 ⋊ C4×#117 |
752 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,14,15,18)(13,17,16,19);(2,3)(8,10,11,9);(4,5,6,7)(13,16)(17,19);(8,9,11,10)(12,13)(14,17)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,d^2=e,b^a=be,h^c=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684584, #10684590, #10685381, … |
| maximal normal subgroup of | #10684584, #10684590, #10685381, … |
| maximal quotient of | Dic3×#376, C4×#4666, C4×#4649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5958);