Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D7×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Hall | C32×C7 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D7 |
| Sylow | C7 ⋊ #3787 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×#157 |
| commutator, hypocenter | C32×C7 | C2×C8 |
| Fitting, socle | C2×C32×C7 | C2×C4 |
| prime radical | C2×C3⋊D21 | C4 |
| cosocle | C7×C3⋊Dic3 | C22 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^4,3^2,7|a^2=d,b^2=c,c^2=d,g^a=g^6,e^b=ef,f^b=ef^2,e^c=e^2,f^c=f^260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 563);