Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5141 |
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ C2×#471 |
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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)(6,8)(7,12)(9,15)(10,16)(11,18)(13,21)(14,17)(19,20);(1,2)(6,7,9,11,10,13,17,19)(8,12,15,18,16,21,14,20);(4,5)(7,11)(8,14)(9,17)(13,19)(15,16)(18,20);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10802045, C4×#5141, #10802104, … |
| maximal normal subgroup of | #10802045, C4×#5141, #10802104, … |
| maximal quotient of | C2×#70846, C2×#70851, C2×#70849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16379);