Finite Group DatabasebetaFinite Group Databasebeta| order | 28736 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×#14267798 |
| Fitting | C42×C449 ⋊ C4 |
| derived, Sylow | C449 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #14267798 |
| commutator, hypocenter | C449 | C43 |
| Frattini | C22 | C22×#14267798 |
| Fitting | C42×C449 | C4 |
| socle | C22×C449 | C22×C4 |
| prime radical, cosocle | C22×D449 | C23 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C42 | |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7184 |
1856 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28736, 1483);