Finite Group DatabasebetaFinite Group Databasebeta| order | 21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1361 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1361 | C16 |
| prime radical | D1361 | C8 |
| cosocle | #24926050 | C2 |
| LCS | G ▷ C1361 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1361 |
Polycyclic presentation:
2^4,1361|a^2=b,b^2=c,c^2=d,e^a=e^574,e^b=e^114,e^c=e^747,e^d=e^1360101 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21776, 54);