Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | H(3,𝔽5) ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4×C5 | #1044 |
| commutator, hypocenter | H(3,𝔽5) | C16 |
| Fitting | C4×H(3,𝔽5) | C4 |
| socle | C2×C5 | #6034 |
| prime radical | C2×H(3,𝔽5) | C8 |
| cosocle | #11758635 | C2 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C4×C5 | |
51 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|a^2=b,b^2=c,c^2=d,e^a=e^3,f^a=f^2,e^b=e^4,f^b=f^4,f^e=fg104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 72);