Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1289 |
228 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 77 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 — 2 generators on 19 points:
(2,3)(4,6)(5,8)(7,11)(9,10)(12,13,15,18,16,19,14,17);(1,2,3)(4,5)(6,10,11,8)(7,9)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,e^2=fg,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1289, C2×#67625, #10685060, … |
| maximal normal subgroup of | D3×#1289, C2×#67625, #10685060, … |
| maximal quotient of | #10681724, #10681735, #10681737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 201);