Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C7×C9 ⋊ D8 |
| Sylow | C9 ⋊ #1141 |
| Sylow | C7 ⋊ #3673 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #92591 |
| commutator, Fitting, cosocle | C4×C7×C9 | C22 |
| Frattini | C3×C4 | D3×D7 |
| socle | C2×C3×C7 | #67 |
| hypercenter | C4 | D7×D9 |
| hypocenter | C7×C9 | D8 |
| LCS | G ▷ C4×C7×C9 ▷ C2×C7×C9 ▷ C7×C9 | |
| UCS | C1 ◁ C2 ◁ C4 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^4,3,7,3|c^2=d,e^3=g,b^a=bc,c^a=cd,f^a=f^6,c^b=cd,e^b=e^2g^2,g^b=g^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 33);