Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4908 |
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#509 |
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7,13,19,9,14,16,17,10,12,20,21,15,18,8,11);(1,2)(7,12)(11,17)(14,18)(19,21);(4,5)(7,11)(8,13)(9,15)(12,17)(14,21)(16,20)(18,19);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712313, #10712315, #10712334, … |
| maximal normal subgroup of | #10712313, #10712315, #10712334, … |
| maximal quotient of | C2×#71440, C2×#71439, C2×#71428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14584);