Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1711 |
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(5,10)(9,17)(11,16)(12,18)(20,22,24,30,23,29,31,35)(21,26,27,28,25,33,32,34);(2,3)(4,6,13,19,8,15,7,14)(5,9,16,18,10,17,11,12)(21,25)(26,33)(27,32)(28,34);(4,5)(6,12)(7,16)(8,10)(9,14)(11,13)(15,18)(17,19)(20,21)(22,28)(23,25)(24,32)(26,30)(27,31)(29,34)(33,35)Polycyclic presentation:
2^7,3|b^2=dfg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1711, C2×#71183, #10782865, … |
| maximal normal subgroup of | D3×#1711, C2×#71183, #10782865, … |
| maximal quotient of | #10688965, #10694930, #10694933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3759);