Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C31 ⋊ D4 |
| Sylow | C31 ⋊ #67 |
| Sylow | C3 ⋊ D124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D31 |
| commutator, Fitting, socle, cosocle | C2×C3×C31 | C22 |
| hypocenter | C3×C31 | D4 |
| LCS | G ▷ C2×C3×C31 ▷ C3×C31 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 372 |
Polycyclic presentation:
2^3,3,31|b^2=c,b^a=bc,e^a=e^30,d^b=d^299 conjugacy classes — view the full character table.
| maximal subgroup of | #13093542, #13093547, #13093549, … |
| maximal normal subgroup of | #13093542, #13093547, #13093549, … |
| maximal quotient of | #13093434, #13093438, #13093439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 16);