Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1945 |
208 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,11,12,20,14,19,13,10)(9,16,17,21,18,15,22,23);(2,3)(5,7)(8,10,13,19,14,20,12,11)(9,15,17,23,18,16,22,21);(2,3)(4,5)(6,7)(8,9,13,17,14,18,12,22)(10,15,19,23,20,16,11,21)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=e,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10711808, #10711809, #10711892, … |
| maximal normal subgroup of | #10711808, #10711809, #10711892, … |
| maximal quotient of | #10693725, #10693730, #10693755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3238);