Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | #393×D131 |
| Fitting | #393×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×#393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D131 |
| commutator, socle, cosocle | C23×C131 | C24 |
| Fitting | #393×C131 | C2 |
| prime radical | C24×D131 | C22 |
| hypercenter | #393 | D131 |
| hypocenter | C131 | C2×#393 |
| LCS | G ▷ C23×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ #393 | |
1036 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4192 |
1474 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 7708);