Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C7 |
No aliases for this group.
| Fitting | C2×C4×C72 ⋊ C2 |
| Sylow | C72 ⋊ C22⋊C4 |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
Polycyclic presentation:
2^4,7^2|b^2=c,b^a=bd,e^a=e^6,f^a=f^6202 conjugacy classes — view the full character table.
| maximal subgroup of | #13096255, #13096270, #13096307, … |
| maximal normal subgroup of | #13096255, #13096270, #13096307, … |
| maximal quotient of | #13096123, #13096124, #13096127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 90);