Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C52 · Schur multiplier (H2) = C22×C5×C8 |
| direct product | C52×#1712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C52 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C52 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C42×C52 ◁ G | |
1120 conjugacy classes of subgroups.
950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5⋊D5×#1712, C52×#19745, #72223235 |
| maximal normal subgroup of | C5⋊D5×#1712, C52×#19745, #72223235 |
Past the SmallGroups library coverage — no SmallGroups id.