Finite Group DatabasebetaFinite Group Databasebeta| order | 21798 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3633 |
| unambiguous semidirect product | C7⋊(C3⋊D519) |
| unambiguous semidirect product | C173⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C173 ⋊ C2 |
| Hall | C32×C173 ⋊ D7 |
| Hall | C7×C173 ⋊ C3⋊D3 |
| Sylow | C173 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D173 |
| Sylow | C32 ⋊ D1211 |
| Sylow | C7 ⋊ C3⋊D519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C173 | C2 |
| LCS | G ▷ C32×C7×C173 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10899 |
Polycyclic presentation:
2,3^2,7,173|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^1725451 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21798, 32);