Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×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^522,f^c=f^5222630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45690198, #45690200, #45690208, … |
| maximal normal subgroup of | #45690198, #45690200, #45690208, … |
| maximal quotient of | #45690050, #45690052, C4⋊C4×Dic523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 104);