Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5142 |
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ C2×#472 |
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) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,8)(7,13)(9,18)(10,16)(11,17)(12,19)(14,21)(15,20);(1,2)(6,7,9,14,11,15,10,12)(8,13,18,21,17,20,16,19);(4,5)(7,12)(8,16)(9,10)(13,20)(14,15)(17,18);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712150, #10712152, #10712213, … |
| maximal normal subgroup of | #10712150, #10712152, #10712213, … |
| maximal quotient of | C2×#70847, C2×#70853, C2×#70848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16380);