Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #102 |
| Sylow | C7 ⋊ #809 |
| Sylow | C3 ⋊ #6395 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=c,b^2=cde,d^2=e,b^a=bd,d^a=de,g^a=g^6,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | #13052281, #13052282, #13052298, … |
| maximal normal subgroup of | #13052281, #13052282, #13052298, … |
| maximal quotient of | #13050866, #13050882, #13050885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 85);