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 ⋊ #919 |
| Sylow | C3 ⋊ #6475 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=e,c^2=de,d^2=e,c^a=cd,d^a=de,g^a=g^6,c^b=cd,d^b=de,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #13052202, #13052218, #13052221, … |
| maximal normal subgroup of | #13052202, #13052218, #13052221, … |
| maximal quotient of | #13053040, #13053041, #13053147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 423);