Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C673 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#19129096 |
| commutator, socle | C2×C673 | C2×C8 |
| Fitting, prime radical | C22×C673 | C8 |
| cosocle | #19129094 | C22 |
| hypercenter | C22 | #19129096 |
| hypocenter | C673 | M32 |
| LCS | G ▷ C2×C673 ▷ C673 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10768 |
Polycyclic presentation:
2^5,673|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^609,f^c=f^58,f^d=f^672356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 242);