Finite Group DatabasebetaFinite Group Databasebeta| order | 36980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C43 |
| unambiguous semidirect product | C43⋊(C43⋊AGL(1,𝔽5)) |
| Fitting, socle, derived, Hall | C5×C432 ⋊ C4 |
| Sylow | C432 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ C43⋊Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C432 | C4 |
| prime radical, cosocle | D5×C432 | C2 |
| LCS | G ▷ C5×C432 | |
| UCS | C1 | |
276 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9245 |
Polycyclic presentation:
2^2,5,43^2|a^2=b,c^a=c^2,d^a=d^42,e^a=e^42,c^b=c^43701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36980, 24);