Finite Group DatabasebetaFinite Group Databasebeta| order | 29504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D461⋊C32 |
| derived, Sylow | C461 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #14270406 |
| commutator, hypocenter | C461 | C2×C32 |
| Frattini | C8 | C2×#14270406 |
| Fitting | C16×C461 | C4 |
| socle | C2×C461 | C2×C16 |
| prime radical | C2×D461 | C16 |
| cosocle | #20301476 | C22 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14752 |
Polycyclic presentation:
2^6,461|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^48,g^b=g^460,g^c=g^4601904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29504, 1480);