Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#5500 |
| Sylow | C3 ⋊ C2×#544 |
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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 — 5 generators on 21 points:
(1,2)(3,4,5)(7,11)(10,13)(14,16,17,21)(15,18,19,20);(6,8)(7,10)(9,12)(11,13);(6,7,9,11)(8,10,12,13);(4,5)(8,12)(10,13)(14,15,17,19)(16,20,21,18);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10687003, #10687006, #10704123, … |
| maximal normal subgroup of | #10687003, #10687006, #10704123, … |
| maximal quotient of | C2×#82156, C2×#82157, C2×#73334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18281);