Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #92517 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C125 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92517 |
| commutator, hypocenter | C125 | C8 |
| Frattini | C2×C25 | AGL(1,𝔽5) |
| Fitting | C2×C125 | C4 |
| socle, prime radical | C2×C5 | #1035 |
| cosocle | Dic125 | C2 |
| LCS | G ▷ C125 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 1000 |
Polycyclic presentation:
2^3,5^3|a^2=b,b^2=c,d^5=e,e^5=f,d^a=d^2ef^2,e^a=e^2f,f^a=f^2,d^b=d^4e^4f^4,e^b=e^4f^4,f^b=f^470 conjugacy classes — view the full character table.
| maximal subgroup of | D125⋊C8, #14522066, C2×#11758618, … |
| maximal normal subgroup of | D125⋊C8, #14522066, C2×#11758618, … |
| maximal quotient of | #14522040, C2×#11758618 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 3);