Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #135 |
| Sylow | C7 ⋊ #912 |
| Sylow | C3 ⋊ #6467 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=e,c^2=de,d^2=e,c^a=cd,d^a=de,g^a=g^6,f^b=f^293 conjugacy classes — view the full character table.
| maximal subgroup of | #13052200, #13052214, #13052215, … |
| maximal normal subgroup of | #13052200, #13052214, #13052215, … |
| maximal quotient of | #13053036, #13053037, #13053122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 417);