Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C523 ⋊ C2 |
| Sylow | C523 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|a^2=e,c^2=d,b^a=bd,f^b=f^5224196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45690159, #45690162, #45690220, … |
| maximal normal subgroup of | #45690159, #45690162, #45690220, … |
| maximal quotient of | #45690051, C4×(C2×D523)⋊C4, C4×Dic523⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 103);