Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5053 |
| Fitting | C2×C3×#123 ⋊ C2 |
| Sylow | C3 ⋊ C2×#458 |
794 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 794 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)(6,9,11,8)(7,13,15,20)(10,18,19,16)(12,14,17,21);(1,2)(6,8)(7,12)(9,11)(10,18)(13,14)(15,17)(16,19)(20,21);(4,5)(6,7)(8,12)(9,17)(10,14)(11,15)(13,18)(16,20)(19,21);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712452, #10712454, #10712466, … |
| maximal normal subgroup of | #10712452, #10712454, #10712466, … |
| maximal quotient of | C2×#71164, C2×#69708, C2×#71168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15468);