Finite Group DatabasebetaFinite Group Databasebeta| order | 25664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C401 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #20264380 |
| commutator, hypocenter | C401 | C2×C32 |
| Frattini | C2 | C2×#20264380 |
| Fitting | C4×C401 | C16 |
| socle | C2×C401 | C2×C16 |
| prime radical | C2×D401 | C16 |
| cosocle | #20264378 | C22 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12832 |
Polycyclic presentation:
2^6,401|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^268,g^b=g^400,g^c=g^45,g^d=g^20,g^e=g^400164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25664, 1678);