Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1803 |
308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(12,13,15,17)(14,19,18,16);(2,3)(8,9,10,11);(4,5,6,7)(9,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^2,e^c=eg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1803, C2×#68904, #10794658, … |
| maximal normal subgroup of | D3×#1803, C2×#68904, #10794658, … |
| maximal quotient of | #10687874, #10687894, #10687914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1480);