Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5245 |
| Fitting | C2×C3×2−1+4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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)(6,8,10,15)(7,12,13,21)(9,18,16,14)(11,19,17,20);(1,2)(6,7)(8,12)(9,17)(10,13)(11,16)(14,19)(15,21)(18,20);(1,2)(4,5)(7,11)(9,16)(12,20)(13,17)(14,18)(19,21);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10712526, #10712536, #10714214, … |
| maximal normal subgroup of | #10712526, #10712536, #10714214, … |
| maximal quotient of | C2×#71888, C2×#71887, C2×#71878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16691);