Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#4541 |
| Sylow | C3 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 77 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 — 3 generators on 21 points:
(3,4,5)(6,8,10,16)(7,11,14,20)(9,18,19,15)(12,13,21,17);(4,5)(6,7,8,12)(9,17,18,20)(10,14,16,21)(11,19,13,15);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682914, #10682915, #10682938, … |
| maximal normal subgroup of | #10682914, #10682915, #10682938, … |
| maximal quotient of | C2×#67643, C2×#67632, #10704465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4308);