Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C17 ⋊ C2 |
| Sylow | C17 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×C22⋊D17 |
| commutator, cosocle | C4×C17 | C23 |
| Frattini | C4 | C22×D17 |
| Fitting | #41×C17 | C2 |
| socle | C2×C17 | C2×D4 |
| hypercenter | #41 | D17 |
| hypocenter | C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #41 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^5,17|d^2=e,c^a=cd,d^a=de,f^a=f^16,c^b=ce,d^c=de91 conjugacy classes — view the full character table.
| maximal subgroup of | #11762977, #11762978, #11762982, … |
| maximal normal subgroup of | #11762977, #11762978, #11762982, … |
| maximal quotient of | #11762810, #11762813, #11762852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 171);