Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #14522937 |
| 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 | D5×C5⋊D5 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
188 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,e^a=e^4,g^a=g^2,e^b=e^3,f^b=f^2,g^c=g^4,e^d=e^4,f^d=f^438 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 900);