Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊C32 |
| derived, Sylow | C23 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D23 |
| commutator, hypocenter | C23 | C32 |
| Fitting, cosocle | C16×C23 | C2 |
| socle, prime radical | C2×C23 | C16 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^5,23|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^22208 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D23, C2×C23⋊C32, #13092250, … |
| maximal normal subgroup of | C32×D23, C2×C23⋊C32, #13092250, … |
| maximal quotient of | C23⋊C64, C2×C23⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 1);