Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C7 ⋊ SD16 |
| Sylow | C32 ⋊ #1143 |
| Sylow | C7 ⋊ #3717 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^4,3^2,7|a^2=c,b^2=d,c^2=d,b^a=bcd,e^a=e^2,g^a=g^6,c^b=cd,f^b=f^2105 conjugacy classes — view the full character table.
| maximal subgroup of | #72245803, #72245808, D7×#3717, … |
| maximal normal subgroup of | #72245803, #72245808, D7×#3717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 373);