Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#4784 |
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ C2×#482 |
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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,8)(7,11)(9,13)(10,12)(15,19)(17,21)(18,20);(1,2)(6,8,9,13)(7,10,12,11)(14,15,16,18)(17,19,21,20);(4,5)(6,7)(8,10)(9,12)(11,13)(15,18)(19,20);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4784, #10802345, #10802410, … |
| maximal normal subgroup of | C4×#4784, #10802345, #10802410, … |
| maximal quotient of | C2×#68873, C2×#68877, C2×#70201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11330);