Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #97 |
| Sylow | C7 ⋊ #815 |
| Sylow | C3 ⋊ #6389 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=c,b^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^6180 conjugacy classes — view the full character table.
| maximal subgroup of | #13050906, #13051416, D7×#815, … |
| maximal normal subgroup of | #13050906, #13051416, D7×#815, … |
| maximal quotient of | #13051358, #13051359, #13051416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 236);