Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#5483 |
| Sylow | C3 ⋊ C2×#543 |
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 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) = 96 |
A minimal faithful permutation representation — 5 generators on 21 points:
(1,2)(3,4,5)(6,8)(7,11)(9,12)(10,13)(14,17,18,16)(15,19,20,21);(6,7)(8,11)(9,10)(12,13)(15,20)(19,21);(8,12)(11,13)(14,16)(15,19)(17,18)(20,21);(4,5)(7,10)(11,13)(14,15,18,20)(16,19,17,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10686998, #10687001, #10704135, … |
| maximal normal subgroup of | #10686998, #10687001, #10704135, … |
| maximal quotient of | C2×#82095, C2×#82094, C2×#73447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18263);