Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5202 |
| Fitting | C2×C3×#137 ⋊ C2 |
| Sylow | C3 ⋊ C2×#455 |
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 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)(6,7,10,13)(8,11,14,20)(9,17,16,12)(15,18,21,19);(1,2)(7,12)(8,14)(9,16)(11,18)(13,17)(19,20);(4,5)(7,11)(9,16)(12,18)(13,20)(15,21)(17,19);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5202, #10801075, #10801112, … |
| maximal normal subgroup of | C4×#5202, #10801075, #10801112, … |
| maximal quotient of | C2×#70972, C2×#70980, C2×#71164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16568);