Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5203 |
| Fitting | C2×C3×#137 ⋊ 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:
(1,2)(3,4,5)(6,8,11,18)(7,13,14,21)(9,17,10,15)(12,20,19,16);(1,2)(6,7)(8,16)(9,12)(10,19)(11,14)(13,17)(15,21)(18,20);(4,5)(7,12)(8,15)(9,10)(14,19)(16,20)(17,18);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10802049, C4×#5203, #10802108, … |
| maximal normal subgroup of | #10802049, C4×#5203, #10802108, … |
| maximal quotient of | C2×#71100, C2×#71036, C2×#71039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16552);