Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C52 · Schur multiplier (H2) = C29×C5 |
| direct product | C52×#3484 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C52 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C52 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ G | |
7600 conjugacy classes of subgroups.
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×#3484 |
| maximal normal subgroup of | C5⋊D5×#3484 |
Past the SmallGroups library coverage — no SmallGroups id.