Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92534 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C5×C25 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92534 |
| commutator, hypocenter | C5×C25 | C16 |
| Frattini | C4×C5 | #1042 |
| Fitting | C4×C5×C25 | C4 |
| socle, prime radical | C2×C52 | #170 |
| cosocle | C5×#6014 | C2 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C4 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|a^2=b,b^2=c,c^2=d,e^5=g,e^a=e^2g,f^a=f^4,g^a=g^2,e^b=e^4g^4,g^b=g^4152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 67);