Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C617 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #14578674 |
| commutator, hypocenter | C617 | C32 |
| Fitting | C8×C617 | C4 |
| socle, prime radical | C2×C617 | C16 |
| cosocle | #23754575 | C2 |
| LCS | G ▷ C617 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19744 |
Polycyclic presentation:
2^5,617|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^194,f^b=f^6161264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 196);