Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#3622 |
| derived, Sylow | C17 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D17 |
| commutator, hypocenter | C17 | C22×C8 |
| Frattini | C4 | C22×D17 |
| Fitting | C22×C4×C17 | C2 |
| socle, prime radical | C23×C17 | C4 |
| cosocle | C4×C17 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11762563, #11762564, #11762571, … |
| maximal normal subgroup of | #11762563, #11762564, #11762571, … |
| maximal quotient of | C2×C4×#3622, C2×C22⋊#3622, C2×C4⋊#3622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 142);