Finite Group DatabasebetaFinite Group Databasebeta| order | 22974 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D547⋊C3)⋊C7 |
| unambiguous semidirect product | (D547⋊C7)⋊C3 |
| unambiguous semidirect product | ((C547⋊C3)⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C547 ⋊ C2×C3×C7 |
| Hall | (C547⋊C3)⋊C7 ⋊ C2 |
| Hall | D547⋊C7 ⋊ C3 |
| Hall | C547⋊C7 ⋊ C2×C3 |
| Hall | D547⋊C3 ⋊ C7 |
| Hall | C547⋊C3 ⋊ C2×C7 |
| Hall | D547 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C547 | C2×C3×C7 |
| LCS | G ▷ C547 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 547 |
Polycyclic presentation:
2,3,7,547|d^a=d^546,d^b=d^40,d^c=d^8155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22974, 30);