Finite Group DatabasebetaFinite Group Databasebeta| order | 25408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D397⋊C32 |
| derived, Sylow | C397 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #13097544 |
| commutator, hypocenter | C397 | C2×C32 |
| Frattini | C8 | C2×#13097544 |
| Fitting | C16×C397 | C4 |
| socle | C2×C397 | C2×C16 |
| prime radical | C2×D397 | C16 |
| cosocle | #20263706 | C22 |
| LCS | G ▷ C397 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12704 |
Polycyclic presentation:
2^6,397|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^334,g^b=g^396,g^c=g^3961648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25408, 1480);