Finite Group DatabasebetaFinite Group Databasebeta| order | 25664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C401 ⋊ C2 |
| Sylow | C401 ⋊ #533 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D401 |
| commutator, socle, cosocle | C22×C401 | C24 |
| Fitting | #125×C401 | C2 |
| prime radical | C22×D401 | C23 |
| hypercenter | #125 | D401 |
| hypocenter | C401 | #533 |
| LCS | G ▷ C22×C401 ▷ C401 | |
| UCS | C1 ◁ C22 ◁ #125 | |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12832 |
Polycyclic presentation:
2^6,401|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^b=g^400,g^c=g^400,g^d=g^4002828 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25664, 1105);