Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C523 ⋊ #126 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|b^2=de,c^2=d,b^a=bd,c^a=ce,f^c=f^5222624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D523, C2×#30660366, #45690732, … |
| maximal normal subgroup of | #126×D523, C2×#30660366, #45690732, … |
| maximal quotient of | #45690072, #45690087, #45690090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 139);