Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C23 ⋊ C2 |
| Sylow | C23 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^5,23|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,f^a=f^22,c^b=ce121 conjugacy classes — view the full character table.
| maximal subgroup of | #13092596, #13092597, #13092601, … |
| maximal normal subgroup of | #13092596, #13092597, #13092601, … |
| maximal quotient of | #13092419, #13092427, #13092459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 104);