Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D5×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C5×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×D25 |
| commutator, hypocenter | C5×C25 | C2×C4 |
| Frattini | C2×C5 | D52 |
| Fitting, cosocle | C2×C5×C25 | C22 |
| socle | C2×C52 | C2×D5 |
| prime radical | C2×C5⋊D25 | C2 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^3,5^3|a^2=c,b^2=c,d^5=f,e^a=e^4,d^b=d^4f^4,f^b=f^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #14522273, #14522275, #14522279, … |
| maximal normal subgroup of | #14522273, #14522275, #14522279, … |
| maximal quotient of | #14522111, #14522113, Dic5×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 37);