Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #137 |
| Sylow | C7 ⋊ #915 |
| Sylow | C3 ⋊ #6481 |
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,g^a=g^6,c^b=cde,d^b=de,f^b=f^263 conjugacy classes — view the full character table.
| maximal subgroup of | #13059207, #13059208, C2×#10620840, … |
| maximal normal subgroup of | #13059207, #13059208, C2×#10620840, … |
| maximal quotient of | #13052990, #13052992, #13053040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 422);