Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ C4×#67 |
| Sylow | C3 ⋊ (C22⋊D7)⋊C4 |
188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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=d,b^2=d,g^a=g^6,c^b=ce,f^b=f^290 conjugacy classes — view the full character table.
| maximal subgroup of | #13058005, #13058006, #13058030, … |
| maximal normal subgroup of | #13058005, #13058006, #13058030, … |
| maximal quotient of | #13053883, #13053894, #13053959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 696);