Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4516 |
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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 — 3 generators on 21 points:
(3,4,5)(6,7,8,15,16,18,21,19,10,12,17,11,9,13,14,20);(4,5)(7,11)(8,14)(9,16)(12,15)(13,20)(17,21)(18,19);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710439, C4×#4516, #10710458, … |
| maximal normal subgroup of | #10710439, C4×#4516, #10710458, … |
| maximal quotient of | C2×#67516, #10704963, #10705194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4017);