Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #92533 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C5×C25 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92533 |
| commutator, hypocenter | C5×C25 | C8 |
| Frattini | C2×C5 | #1042 |
| Fitting | C2×C5×C25 | C4 |
| socle, prime radical | C2×C52 | Dic5 |
| cosocle | Dic5×C25 | C2 |
| LCS | G ▷ C5×C25 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^3,5^3|a^2=b,b^2=c,d^5=f,d^a=d^4f^4,e^a=e^3,f^a=f^4,e^b=e^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #170×D25, #14522273, #14522274, … |
| maximal normal subgroup of | #170×D25, #14522273, #14522274, … |
| maximal quotient of | #14522103, C2×#11758643 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 28);