Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2153 |
152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(6,16)(11,25)(15,29)(17,19)(18,31)(24,32)(26,34)(30,35);(2,3)(4,6,7,17,10,16,9,19)(5,11,12,15,14,25,20,29)(8,18,21,24,23,31,22,32)(13,26,27,30,28,34,33,35);(4,5,8,13,9,12,22,27,10,14,23,28,7,20,21,33)(6,15,18,30,19,25,32,34,16,29,31,35,17,11,24,26)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10711301, #10711302, #10711305, … |
| maximal normal subgroup of | #10711301, #10711302, #10711305, … |
| maximal quotient of | #10706734, #10706736, #10706760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3999);