Finite Group DatabasebetaFinite Group Databasebeta| order | 28900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C289 · Schur multiplier (H2) = C1 |
| direct product | #1042×C289 |
| Fitting, Hall | C52×C289 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | #1042 |
| commutator, hypocenter | C52 | C4×C289 |
| Frattini | C17 | C17×#1042 |
| Fitting | C52×C289 | C4 |
| socle | C52×C17 | C4×C17 |
| prime radical, cosocle | C5×D5×C17 | C2×C17 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C289 | |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5780 |
3757 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28900, 36);