Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ #124 |
| Sylow | C7 ⋊ #885 |
| Sylow | C3 ⋊ #6438 |
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=e,c^2=d,b^a=bd,c^a=ce,g^a=g^6,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | #13057739, #13057744, #13057789, … |
| maximal normal subgroup of | #13057739, #13057744, #13057789, … |
| maximal quotient of | #13053266, #13053280, #13053282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 497);