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 ⋊ #837 |
| Sylow | C3 ⋊ #6411 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|a^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^6,d^b=de114 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#837, D3×#6411, #13054804, … |
| maximal normal subgroup of | D7×#837, D3×#6411, #13054804, … |
| maximal quotient of | #13051435, D4⋊(C3⋊(C7⋊C8)), #13051439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 258);