Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1951 |
196 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 93 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:
(1,2,3)(8,10,12,17,13,19,11,18)(9,15,14,21,16,22,20,23);(4,6,7,5)(8,9)(10,15)(11,20)(12,14)(13,16)(17,21)(18,23)(19,22);(2,3)(4,5,7,6)(9,14)(10,17)(11,12)(15,22)(16,20)(18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10711870, #10711873, #10711898, … |
| maximal normal subgroup of | #10711870, #10711873, #10711898, … |
| maximal quotient of | #10693798, #10693808, #10693818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2469);