Finite Group DatabasebetaFinite Group Databasebeta| order | 2577 |
| isoclinism | isoclinic class of C859⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C859⋊C3 |
| Fitting, socle, derived, Sylow | C859 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C859 | C3 |
| LCS | G ▷ C859 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 859 |
| transitive degree | μt(G) = 859 |
Polycyclic presentation:
3,859|b^a=b^260289 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C859⋊C3, C7×C859⋊C3, #31825202, … |
| maximal normal subgroup of | C5×C859⋊C3, C7×C859⋊C3, (C859⋊C3)⋊C11, … |
| maximal quotient of | C5×C859⋊C3, C7×C859⋊C3, #31825202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2577, 1);