Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5062 |
| Fitting | C2×C3×#124 ⋊ C2 |
| Sylow | C3 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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)(7,12)(9,18)(10,16)(11,17)(13,21)(14,20)(15,19);(1,2)(6,8,10,16)(7,11,14,21)(9,18,19,15)(12,17,20,13);(4,5)(6,7)(8,11)(9,17)(10,14)(12,15)(13,19)(16,21)(18,20);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712527, #10712529, #10712537, … |
| maximal normal subgroup of | #10712527, #10712529, #10712537, … |
| maximal quotient of | C2×#69702, C2×#69717, C2×#69703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15527);