Finite Group DatabasebetaFinite Group Databasebeta| order | 19744 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C617 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D617 |
| commutator | C2×C617 | C42 |
| Fitting | C22×C4×C617 | C2 |
| socle, prime radical, cosocle | C23×C617 | C22 |
| hypercenter | C22×C4 | D617 |
| hypocenter | C617 | #95 |
| LCS | G ▷ C2×C617 ▷ C617 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19744 |
Polycyclic presentation:
2^5,617|a^2=d,b^2=e,b^a=bc,f^b=f^6164948 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19744, 53);