Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4749 |
| Fitting | C2×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ C2×#472 |
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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:
(3,4,5)(7,12)(9,16)(11,17)(13,20)(14,21)(18,19);(6,8,9,14,10,15,16,21)(7,11,12,18,13,19,20,17);(1,2)(4,5)(6,7)(8,11)(9,12)(10,13)(14,18)(15,19)(16,20)(17,21);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4749, #10802066, #10802087, … |
| maximal normal subgroup of | C4×#4749, #10802066, #10802087, … |
| maximal quotient of | C2×#68395, C2×#68497, C2×#68396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11278);