Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D52⋊D5 |
| commutator, cosocle | C5×#1039 | C22 |
| Fitting, socle | C2×C53 | D4 |
| hypocenter | C53 | D8 |
| LCS | G ▷ C5×#1039 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^4,5^3|a^2=c,c^2=d,b^a=bc,e^a=e^2,f^a=f^3,g^a=g^4,c^b=cd,e^b=f,f^b=e,e^c=e^4,f^c=f^483 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 718);