Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1770 |
272 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 157 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:
(1,2,3)(12,14,19,17,15,18,16,13);(2,3)(4,5,6,7)(9,11)(13,17)(14,18);(8,9,10,11)(12,13,16,18,15,17,19,14)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,c^b=cg,h^b=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682092, #10682093, #10682098, … |
| maximal normal subgroup of | #10682092, #10682093, #10682098, … |
| maximal quotient of | #10686312, #10686316, #10686338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2333);