Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C491 ⋊ C2 |
| Sylow | C491 ⋊ #135 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^490,d^b=de,f^b=f^4903934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536531, #44536533, #44536534, … |
| maximal normal subgroup of | #44536531, #44536533, #44536534, … |
| maximal quotient of | #44536722, #44536763, C4×D3928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 168);