Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of C5⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C53 |
| direct product | C22×#92553 |
| derived, Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C5⋊(C5⋊D5) |
| commutator, hypocenter | C53 | C22×C4 |
| Frattini | C2 | C22×C5⋊(C5⋊D5) |
| Fitting, socle, prime radical | C23×C53 | C2 |
| cosocle | C2×C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23 | |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2000 |
512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 890);