Finite Group DatabasebetaFinite Group Databasebeta| order | 21996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D141⋊D39 |
| Fitting, socle, derived, Hall | C32×C13×C47 ⋊ C22 |
| Hall | C13×C47 ⋊ D32 |
| Hall | C32×C47 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D47 |
| Sylow | C47 ⋊ D3×D39 |
| Sylow | C13 ⋊ (C3⋊D3)⋊D47 |
| Sylow | C32 ⋊ D13×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C47 | C22 |
| LCS | G ▷ C32×C13×C47 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3666 |
Polycyclic presentation:
2^2,3^2,13,47|d^a=d^2,f^a=f^46,c^b=c^2,d^b=d^2,e^b=e^121443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21996, 103);