Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C7×C8 ⋊ C2 |
| Hall | C3×C7 ⋊ #131 |
| Sylow | C7 ⋊ #901 |
| Sylow | C3 ⋊ #6464 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^6180 conjugacy classes — view the full character table.
| maximal subgroup of | #13050917, #13050918, #13051411, … |
| maximal normal subgroup of | #13050917, #13050918, #13051411, … |
| maximal quotient of | C8×Dic42, #13056316, C8×D84, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 966);