Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4753 |
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,9,18,21,11,19,10,12)(7,8,15,20,14,17,13,16);(1,2)(6,8,11,17)(7,12,14,21)(9,15,19,13)(10,20,18,16);(4,5)(6,7)(8,12)(9,16)(10,15)(11,14)(13,18)(17,21)(19,20);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10712528, #10712538, #10714216, … |
| maximal normal subgroup of | #10712528, #10712538, #10714216, … |
| maximal quotient of | C2×#68130, C2×#68136, C2×#68131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11283);