Finite Group DatabasebetaFinite Group Databasebeta| order | 36980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C43 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C432 ⋊ C4 |
| Sylow | C432 ⋊ Dic5 |
| Sylow | C5 ⋊ #20301711 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C432 | C4 |
| prime radical, cosocle | C5×C43⋊D43 | C2 |
| LCS | G ▷ C5×C432 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 430 |
Polycyclic presentation:
2^2,5,43^2|a^2=b,c^a=c^4,d^a=d^41e^31,e^a=d^4e^2,d^b=d^42,e^b=e^422318 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36980, 25);