Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #6053⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6053⋊D5 |
| Fitting, socle, Sylow | C53 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator | C5×C5⋊D5 | C2×C4 |
| Fitting, socle, hypocenter | C53 | M16 |
| prime radical | #92566 | C4 |
| cosocle | C5×#1043 | C22 |
| LCS | G ▷ C5×C5⋊D5 ▷ C53 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^4,5^3|b^2=c,c^2=d,b^a=bd,e^a=e^4,g^a=g^4,e^b=f^2,f^b=e,e^c=e^2,f^c=f^2,e^d=e^4,f^d=f^435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 915);