Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C197 ⋊ #2857 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D197 |
| commutator, socle, cosocle | C23×C197 | C24 |
| Fitting | #380×C197 | C2 |
| prime radical | C24×C197 | C23 |
| hypercenter | #380 | D197 |
| hypocenter | C197 | #2857 |
| LCS | G ▷ C23×C197 ▷ C197 | |
| UCS | C1 ◁ C23 ◁ #380 | |
644 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12608 |
Polycyclic presentation:
2^7,197|a^2=e,b^2=e,c^2=f,b^a=be,c^a=cf,d^a=dg,h^b=h^1962788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 12860);