Finite Group DatabasebetaFinite Group Databasebeta| order | 31244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C107⋊#64408 |
| Fitting, socle, derived, Hall | C73×C107 ⋊ C4 |
| Sylow | C107 ⋊ #64408 |
| Sylow | C73 ⋊ Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73×C107 | C4 |
| prime radical, cosocle | C107×D73 | C2 |
| LCS | G ▷ C73×C107 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7811 |
Polycyclic presentation:
2^2,73,107|a^2=b,c^a=c^27,d^a=d^106,c^b=c^722036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31244, 7);