Finite Group DatabasebetaFinite Group Databasebeta| order | 1744 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D109 |
| commutator, hypocenter | C109 | C16 |
| Fitting, cosocle | C8×C109 | C2 |
| socle, prime radical | C2×C109 | C8 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 1744 |
Polycyclic presentation:
2^4,109|a^2=b,b^2=c,c^2=d,e^a=e^108448 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D109, C2×#13182004, #16812638, … |
| maximal normal subgroup of | C16×D109, C2×#13182004, #16812638, … |
| maximal quotient of | #16812605, C2×#13182004 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1744, 15);