Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4⋊C8 |
| Sylow | C7 ⋊ Dic3⋊C8 |
| Sylow | C3 ⋊ Dic7⋊C8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=d,b^2=c,c^2=e,b^a=bd,f^a=f^2,g^a=g^6180 conjugacy classes — view the full character table.
| maximal subgroup of | D7×Dic3⋊C8, #13052945, #13052948, … |
| maximal normal subgroup of | D7×Dic3⋊C8, #13052945, #13052948, … |
| maximal quotient of | #13051383, #13051384, #13051405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 235);