Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4891 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C2×#478 |
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 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)(7,11)(10,13)(14,15,16,18,17,20,21,19);(1,2)(6,8,9,12)(7,10,11,13)(15,19)(16,21)(18,20);(4,5)(6,7)(8,10)(9,11)(12,13)(15,18)(16,21)(19,20);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10802792, C4×#4891, #10802866, … |
| maximal normal subgroup of | #10802792, C4×#4891, #10802866, … |
| maximal quotient of | C2×#68893, C2×#70638, C2×#68895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11737);