Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C7 ⋊ #124 |
| Sylow | C7 ⋊ #875 |
| Sylow | C3 ⋊ #6499 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=d,c^2=e,b^a=bde,g^a=g^6,c^b=ce,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13052661, #13052662, #13052663, … |
| maximal normal subgroup of | #13052661, #13052662, #13052663, … |
| maximal quotient of | #13052277, #13052278, #13052279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 517);