Finite Group DatabasebetaFinite Group Databasebeta| order | 31205 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C79 |
| unambiguous semidirect product | C792⋊C5 |
| Fitting, socle, derived, Sylow | C792 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C792 | C5 |
| LCS | G ▷ C792 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 395 |
Polycyclic presentation:
5,79^2|b^a=b^36c^56,c^a=b^69c^131253 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31205, 2);