Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#4451 |
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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)(6,7)(8,13)(9,11)(10,12)(14,15,16,19)(17,18,20,21);(4,5)(7,10)(8,12)(11,13)(15,18)(16,20);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10686060, C4×#4451, #10686070, … |
| maximal normal subgroup of | #10686060, C4×#4451, #10686070, … |
| maximal quotient of | C2×#67479, C2×#67478, #10683144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1973);