Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C5 |
| direct product | C23×#6057 |
| Fitting, socle | C23×C52 ⋊ Q8 |
| Sylow | C52 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #6057 |
| commutator, cosocle | C5⋊D5 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | Q8 |
| prime radical | C23×C5⋊D5 | C22 |
| hypocenter | C52 | C23×Q8 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C23 | |
1204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10272);