Finite Group DatabasebetaFinite Group Databasebeta| order | 5622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D937⋊C3 |
| unambiguous semidirect product | (C937⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C937 ⋊ C2×C3 |
| Hall | C937⋊C3 ⋊ C2 |
| Hall | D937 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C937 | C2×C3 |
| LCS | G ▷ C937 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,937|c^a=c^936,c^b=c^614162 conjugacy classes — view the full character table.
| maximal subgroup of | #16836713⋊C3, C2×D937⋊C3, #22554625⋊C2, … |
| maximal normal subgroup of | #16836713⋊C3, C2×D937⋊C3, #22554625⋊C2, … |
| maximal quotient of | Dic937⋊C3, C2×D937⋊C3, #22554623⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5622, 1);