Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ C2×Q16 |
| Sylow | C7 ⋊ D3×Q16 |
| Sylow | C3 ⋊ D7×Q16 |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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|a^2=e,b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^6,c^b=cd,d^b=de,f^b=f^2,d^c=de57 conjugacy classes — view the full character table.
| maximal subgroup of | #13059298, #13059307, #13059319, … |
| maximal normal subgroup of | #13059298, #13059307, #13059319, … |
| maximal quotient of | #13052525, #13052583, #13052587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 655);