Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of C5⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C53 |
| direct product | C23×C5⋊(C5⋊D5) |
| Fitting, socle | C23×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C5⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C53 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23 | |
4288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1000 |
512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 962);