Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #1797 |
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(5,7);(2,3)(8,9,10,11);(4,5)(6,7)(9,11)(12,13,14,16,15,17,18,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,f^2=g,b^a=bd,c^a=ce,h^b=h^2,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10683170, #10683174, #10683183, … |
| maximal normal subgroup of | #10683170, #10683174, #10683183, … |
| maximal quotient of | #10687843, #10687847, #10687851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1238);