Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C23 ⋊ C2 |
| Sylow | C23 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 184 |
Polycyclic presentation:
2^5,23|b^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^22,c^b=ce,d^c=de121 conjugacy classes — view the full character table.
| maximal subgroup of | #13092583, #13092584, #13092588, … |
| maximal normal subgroup of | #13092583, #13092584, #13092588, … |
| maximal quotient of | #13092416, #13092422, #13092457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 127);