Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊(C7⋊C8)) |
| Hall | C3×C7 ⋊ C4⋊C8 |
| Sylow | C7 ⋊ C4⋊(C3⋊C8) |
| Sylow | C3 ⋊ C4⋊(C7⋊C8) |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^2,g^a=g^6180 conjugacy classes — view the full character table.
| maximal subgroup of | #13050863, #13050865, #13050869, … |
| maximal normal subgroup of | #13050863, #13050865, #13050869, … |
| maximal quotient of | #13051360, #13051361, C4⋊(C3⋊(C7⋊C16)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 225);