Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C673 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #24924657 |
| commutator, hypocenter | C673 | C32 |
| Fitting, socle, prime radical | C2×C673 | C16 |
| cosocle | #24924655 | C2 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21536 |
Polycyclic presentation:
2^5,673|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^464,f^b=f^609,f^c=f^58,f^d=f^672116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 245);