Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1628 |
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,8,7)(5,9,10,11)(12,14)(13,15)(16,19)(17,18);(2,3)(4,5)(6,9)(7,11)(8,10)(12,13,17,19)(14,15,18,16);(5,9)(6,7)(10,11)(13,14)(15,16)(18,19)Polycyclic presentation:
2^7,3|b^2=g,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,h^b=h^2,d^c=dg,e^c=eg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1628, C2×#71019, #10770944, … |
| maximal normal subgroup of | D3×#1628, C2×#71019, #10770944, … |
| maximal quotient of | #10683920, #10683940, #10683948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3595);