Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #14522942 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting, socle, Sylow | C53 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator | C5×C5⋊D5 | C2×C4 |
| Fitting, socle, hypocenter | C53 | C22⋊C4 |
| prime radical | D53 | C2 |
| cosocle | D5×C5⋊D5 | C22 |
| LCS | G ▷ C5×C5⋊D5 ▷ C53 | |
| UCS | C1 | |
168 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 17 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^a=bd,e^a=e^2,f^a=f^3,g^a=g^2,e^b=f,f^b=e,e^c=e^4,f^c=f^4,g^c=g^4,e^d=e^4,f^d=f^444 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 905);