Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1848 |
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(4,5,6,7);(1,2,3)(8,10,11,18,13,20,12,19)(9,14,15,17,16,22,21,23);(5,7)(8,9,12,15,13,16,11,21)(10,17,19,22,20,23,18,14)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10711246, #10711247, #10711261, … |
| maximal normal subgroup of | #10711246, #10711247, #10711261, … |
| maximal quotient of | #10688923, #10688926, #10688929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3269);