Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1599 |
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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 — 3 generators on 19 points:
(1,2,3)(4,6,7,10)(5,8,9,11);(2,3)(4,5)(6,8)(7,9)(10,11)(12,13,15,17)(14,19,18,16);(8,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|b^2=f,c^2=g,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=eg,h^b=h^2,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10707938, #10707939, #10707949, … |
| maximal normal subgroup of | #10707938, #10707939, #10707949, … |
| maximal quotient of | #10683913, #10683926, #10683957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2280);