Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1811 |
272 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 272 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) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7)(10,18)(14,22)(17,23)(19,20);(2,3)(8,10,11,19,13,18,12,20)(9,14,15,17,16,22,21,23);(4,5)(6,7)(8,9,12,15,13,16,11,21)(10,17,20,22,18,23,19,14)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1811, C2×#69983, #10794809, … |
| maximal normal subgroup of | D3×#1811, C2×#69983, #10794809, … |
| maximal quotient of | #10688028, #10688033, #10688037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2559);