Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5078 |
| Sylow | C3 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 197 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) = 384 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,8,9,13)(7,10,11,12)(15,18)(16,21)(19,20);(6,7,9,11)(8,12,13,10);(4,5)(14,15,16,19,17,20,21,18);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10690440, #10690441, #10690443, … |
| maximal normal subgroup of | #10690440, #10690441, #10690443, … |
| maximal quotient of | C2×#69577, C2×#69619, C2×#69582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15781);