Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C23 ⋊ C2 |
| Sylow | C23 ⋊ #100 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 184 |
Polycyclic presentation:
2^5,23|b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^22,d^b=de121 conjugacy classes — view the full character table.
| maximal subgroup of | #100×D23, C2×#10625005, #13092399, … |
| maximal normal subgroup of | #100×D23, C2×#10625005, #13092399, … |
| maximal quotient of | #13092140, #13092156, #13092160, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 29);