Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1966 |
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 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:
(1,2,3)(4,5,6,7);(2,3)(8,10,16,18,12,17,11,19)(9,13,15,23,14,21,22,20);(2,3)(5,7)(8,9,11,15,12,14,16,22)(10,13,18,20,17,21,19,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,c^2=e,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg,f^b=fg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10687409, #10687411, #10687426, … |
| maximal normal subgroup of | #10687409, #10687411, #10687426, … |
| maximal quotient of | #10694016, #10694034, #10694196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4365);