Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5087 |
| Fitting | C2×C3×C4⋊Q8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#474 |
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7)(8,13)(9,11)(10,12)(14,16,17,21)(15,18,19,20);(1,2)(14,15,17,19)(16,20,21,18);(4,5)(7,10)(8,12)(11,13);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10689973, #10689979, #10689994, … |
| maximal normal subgroup of | #10689973, #10689979, #10689994, … |
| maximal quotient of | C2×#69584, C2×#69625, C2×#69600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15786);