Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #11758779 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C53 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C8 |
| prime radical | C5×C5⋊D5 | C4 |
| cosocle | #92561 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^3,5^3|a^2=b,b^2=c,d^a=de^2,e^a=de^4,f^a=f^2,d^b=d^3,e^b=e^3,f^b=f^4,d^c=d^4,e^c=e^425 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#6053, #14522948, #14522950, … |
| maximal normal subgroup of | D5⋊#6053, #14522948, #14522950, … |
| maximal quotient of | #14522664, C2×#11758779 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 164);