Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C7 ⋊ #101 |
| Sylow | C7 ⋊ #836 |
| Sylow | C3 ⋊ #6398 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=e,b^2=c,c^2=e,b^a=bd,c^a=ce,g^a=g^6,d^b=de,f^b=f^275 conjugacy classes — view the full character table.
| maximal subgroup of | #13052499, #13052500, #13053451, … |
| maximal normal subgroup of | #13052499, #13052500, #13053451, … |
| maximal quotient of | #13050877, #13050883, #13050886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 78);