Finite Group DatabasebetaFinite Group Databasebeta| order | 31719 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C97×C109 ⋊ C3 |
| Sylow | C109 ⋊ C97⋊C3 |
| Sylow | C97 ⋊ C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C97×C109 | C3 |
| LCS | G ▷ C97×C109 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10573 |
Polycyclic presentation:
3,97,109|b^a=b^61,c^a=c^453527 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31719, 4);