Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D523)⋊C8 |
| Fitting | C2×C8×C523 ⋊ C2 |
| Sylow | C523 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|a^2=d,d^2=e,b^a=bc,f^b=f^5224196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D523, C2×(C2×D523)⋊C8, #45690167, … |
| maximal normal subgroup of | C22⋊C8×D523, C2×(C2×D523)⋊C8, #45690167, … |
| maximal quotient of | #45689928, #45689930, #45689932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 58);