Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2285 |
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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)(8,9,10,11);(13,16)(17,19);(4,5,6,7)(9,11)(12,13)(14,17)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10700986, #10700990, #10700996, … |
| maximal normal subgroup of | #10700986, #10700990, #10700996, … |
| maximal quotient of | #10716294, #10716302, C4×#4942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14800);