Finite Group DatabasebetaFinite Group Databasebeta| order | 1744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C109 ⋊ C2 |
| Sylow | C109 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D109 |
| commutator, socle | C2×C109 | C2×C4 |
| Fitting | C8×C109 | C2 |
| prime radical | C2×D109 | C4 |
| cosocle | C4×C109 | C22 |
| hypercenter | C8 | D109 |
| hypocenter | C109 | M16 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 872 |
Polycyclic presentation:
2^4,109|a^2=c,c^2=d,b^a=bd,e^b=e^108442 conjugacy classes — view the full character table.
| maximal subgroup of | M16×D109, C2×#13182012, #16812705, … |
| maximal normal subgroup of | M16×D109, C2×#13182012, #16812705, … |
| maximal quotient of | #16812609, #16812611, #16812628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1744, 23);