Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#3622 |
| derived, Sylow | C17 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D17 |
| commutator, hypocenter | C17 | C4×C8 |
| Frattini | C2×C4 | C2×D17 |
| Fitting | C42×C17 | C2 |
| socle, prime radical | C22×C17 | C2×C4 |
| cosocle | C2×C4×C17 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#3622, #11762530, #11762531, … |
| maximal normal subgroup of | C8×#3622, #11762530, #11762531, … |
| maximal quotient of | C8×#3622, #11762530, #11762564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 9);