Finite Group DatabasebetaFinite Group Databasebeta| order | 2560 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×#347042 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #2846 |
| commutator, Frattini, cosocle | C25 | C24×C5 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C25×C5 ◁ G | |
7756 conjugacy classes of subgroups; only the 392 normal subgroups are shown.
This group has 7756 conjugacy classes of subgroups — too many to draw. Only its 392 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
295 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | D5×#347042, AGL(1,𝔽5)×#347042 |
| maximal subgroup of | D5×#347042, C5×#72209641 |
| maximal normal subgroup of | D5×#347042 |
Past the SmallGroups library coverage — no SmallGroups id.