Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #104 |
| Sylow | C7 ⋊ #805 |
| Sylow | C3 ⋊ #6411 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|a^2=c,d^2=e,b^a=bd,g^a=g^6,c^b=ce,d^b=de,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#805, #13052488, #13053357, … |
| maximal normal subgroup of | D7×#805, #13052488, #13053357, … |
| maximal quotient of | #13050865, #13050871, #13050875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 96);