Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×C5×#168 |
| derived | C5 ⋊ C23×C5×C8 |
| Sylow | C52 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4×C5 | D5 |
| commutator, hypocenter | C5 | C23×C5×C8 |
| Frattini | C4 | C23×C5×D5 |
| Fitting | C23×C4×C52 | C2 |
| socle, prime radical | C24×C52 | C4 |
| cosocle | C4×C5 | C24×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C4×C5 | |
912 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#87767, C22×C5×#3935, C22×#11716596 |
| maximal normal subgroup of | C23×#87767, C22×C5×#3935, C22×#11716596 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9286);