Finite Group DatabasebetaFinite Group Databasebeta| order | 28773 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C23 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C139 ⋊ C3×C23 |
| derived, Sylow | C139 ⋊ C32×C23 |
| Hall | C139⋊C23 ⋊ C32 |
| Hall | C3×C139⋊C3 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C139⋊C3)⋊C23 |
| commutator, cosocle, hypocenter | C139 | C32×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C139 | C3×C23 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 417 |
213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28773, 6);