Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2048 |
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(4,6,7,14,9,15,8,13)(5,11,10,17,12,18,16,19);(1,2,3)(4,5)(6,11)(7,16)(8,10)(9,12)(13,17)(14,19)(15,18);(5,10)(6,13)(7,8)(11,18)(12,16)(14,15)Polycyclic presentation:
2^7,3|c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,f^c=fg,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2048, C2×#72092, #10823029, … |
| maximal normal subgroup of | D3×#2048, C2×#72092, #10823029, … |
| maximal quotient of | #10698750, #10698757, #10698764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4668);