Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5198 |
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ C2×#453 |
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(1,2)(3,4,5)(7,10)(8,13)(11,12);(1,2)(6,7)(8,10)(9,11)(12,13);(4,5)(8,13)(10,12);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5198, #10801064, #10801101, … |
| maximal normal subgroup of | C4×#5198, #10801064, #10801101, … |
| maximal quotient of | C2×#70968, C2×#70976, C2×#71168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16532);