Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #92586 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#92591 |
| Hall | C7×C9 ⋊ C2×D4 |
| Sylow | C9 ⋊ C2×C22⋊D7 |
| Sylow | C7 ⋊ C2×#611 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×D9 |
| commutator, cosocle | C2×C7×C9 | C23 |
| Frattini | C2×C3 | C2×D3×D7 |
| Fitting | C22×C7×C9 | C22 |
| socle | C22×C3×C7 | C2×D3 |
| hypocenter | C7×C9 | C2×D4 |
| LCS | G ▷ C2×C7×C9 ▷ C7×C9 | |
| UCS | C1 ◁ C22 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 168);