Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C337 ⋊ C2 |
| Sylow | C337 ⋊ #123 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|c^2=d,b^a=bd,c^a=ce,f^a=f^336,f^c=f^3361694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341496, #123×D337, C2×#24924943, … |
| maximal normal subgroup of | #36341496, #123×D337, C2×#24924943, … |
| maximal quotient of | #36341166, #36341180, #36341182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 130);