Finite Group DatabasebetaFinite Group Databasebeta| order | 31100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C311⋊C5)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C311⋊AGL(1,𝔽5))⋊C5 |
| Fitting, socle, derived | C5×C311 ⋊ C4×C5 |
| Hall | C5×C311⋊C5 ⋊ C4 |
| Sylow | C311 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C311 | C4×C5 |
| prime radical | D5×C311⋊C5 | C2 |
| cosocle | D5×C311 | C2×C5 |
| LCS | G ▷ C5×C311 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1555 |
Polycyclic presentation:
2,5,2,5,311|a^2=c,d^a=d^2,e^a=e^310,e^b=e^36,d^c=d^4149 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31100, 27);