Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #14522938 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C53 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C42 |
| prime radical, cosocle | #92566 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,e^a=e^2,g^a=g^2,e^b=e^2,f^b=f^2,e^c=e^4,g^c=g^4,e^d=e^4,f^d=f^435 conjugacy classes — view the full character table.
| maximal subgroup of | #72228947 |
| maximal normal subgroup of | #72228947 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 901);