Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #1161 ⋊ C9 |
| Sylow | C7 ⋊ #41⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | A4×D7 |
| commutator, hypocenter | C7×Q8 | C2×C9 |
| Fitting, cosocle | C3×C7×Q8 | C2×C3 |
| socle | C2×C3×C7 | C2×A4 |
| prime radical | C3×#1161 | C3 |
| LCS | G ▷ C7×Q8 | |
| UCS | C1 ◁ C2×C3 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2,3^2,2^2,7,2|a^2=g,b^3=c,d^2=g,e^2=g,f^a=f^6,d^b=de,e^b=d,e^d=eg105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 140);