Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C197 · Schur multiplier (H2) = C29 |
| direct product | C22×#123×C197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C197 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C197 |
| prime radical | C23×D4×C197 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C197 ◁ G | |
1968 conjugacy classes of subgroups; only the 952 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 952 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12608 |
11032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 2166);