Finite Group DatabasebetaFinite Group Databasebeta| order | 21812 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C19⋊#4223) |
| unambiguous semidirect product | C19⋊(C7⋊#4223) |
| Fitting, socle, derived, Hall | C7×C19×C41 ⋊ C4 |
| Hall | C19×C41 ⋊ Dic7 |
| Hall | C7×C41 ⋊ Dic19 |
| Hall | C7×C19 ⋊ #4223 |
| Sylow | C41 ⋊ Dic133 |
| Sylow | C19 ⋊ C7⋊#4223 |
| Sylow | C7 ⋊ C19⋊#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C19×C41 | C4 |
| prime radical, cosocle | C7×C19×D41 | C2 |
| LCS | G ▷ C7×C19×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5453 |
Polycyclic presentation:
2^2,7,19,41|a^2=b,c^a=c^6,d^a=d^18,e^a=e^32,e^b=e^401466 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21812, 15);