Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1300 |
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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) = 96 |
A minimal faithful permutation representation — 2 generators on 19 points:
(2,3)(5,8,10,9)(12,14)(13,16)(15,17)(18,19);(1,2,3)(4,5)(6,8)(7,10)(9,11)(12,13,15,18,16,14,19,17)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1300, C2×#67748, #10685381, … |
| maximal normal subgroup of | D3×#1300, C2×#67748, #10685381, … |
| maximal quotient of | #10681742, #10681745, #10681751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 324);