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 ⋊ #2326 |
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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);(8,9,10,11)(13,16)(17,19);(2,3)(4,6,7,5)(12,13)(14,17)(15,16)(18,19);(2,3)(4,5,7,6)(9,11)(13,16)(14,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10710359, #10710379, #10711180, … |
| maximal normal subgroup of | #10710359, #10710379, #10711180, … |
| maximal quotient of | #10716450, #10716492, #10716499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15529);