Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#5067 |
| Fitting | C2×C3×#125 ⋊ C2 |
| Sylow | C3 ⋊ C2×#490 |
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7)(8,13)(9,11)(10,12)(14,16,17,21)(15,19,18,20);(1,2)(7,11)(10,13)(14,15,17,18)(16,20,21,19);(4,5)(7,10)(8,12)(11,13)(15,18)(19,20);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10690119, #10690121, #10696472, … |
| maximal normal subgroup of | #10690119, #10690121, #10696472, … |
| maximal quotient of | C2×#69548, C2×#69617, C2×#69553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15586);