Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92535 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| derived, Sylow | H(3,𝔽5) ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92535 |
| commutator, hypocenter | H(3,𝔽5) | C2×C8 |
| Frattini, socle | C2×C5 | C2×#1042 |
| Fitting | C4×H(3,𝔽5) | C4 |
| prime radical | C2×(C5⋊D5)⋊C5 | C4 |
| cosocle | #1039⋊C5 | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C4 | |
83 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,c^2=d,e^a=e^2,f^a=f^4,g^a=g^3,e^c=e^4,g^c=g^4,f^e=fg56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 310);