Finite Group DatabasebetaFinite Group Databasebeta| order | 21717 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C127 ⋊ C9 |
| Sylow | C127 ⋊ #4294 |
| Sylow | C19 ⋊ #11765917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #20299746 |
| commutator, hypocenter | C19×C127 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C19×C127 | C3 |
| LCS | G ▷ C19×C127 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21717 |
Polycyclic presentation:
3,19,127,3|a^3=d,b^a=b^7,c^a=c^192421 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21717, 4);