Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5177 |
| Fitting | C22×C3×SD16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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)(7,12)(8,15)(9,17)(11,18)(13,14)(16,21);(1,2)(6,8,9,15,10,16,17,21)(7,11,12,20,14,18,13,19);(1,2)(4,5)(6,7)(8,11)(9,12)(10,14)(13,17)(15,20)(16,18)(19,21);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5177, #10802055, #10802105, … |
| maximal normal subgroup of | C4×#5177, #10802055, #10802105, … |
| maximal quotient of | C2×#71267, C2×#71344, C2×#71201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16444);