Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#63214 |
| derived, Sylow | C17 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D17 |
| commutator, hypocenter | C17 | C2×C16 |
| Frattini | C8 | C2×D17 |
| Fitting | C2×C8×C17 | C2 |
| socle, prime radical | C22×C17 | C8 |
| cosocle | C8×C17 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C16×Dic17, C4×#63214, #11762584, … |
| maximal normal subgroup of | C16×Dic17, C4×#63214, #11762584, … |
| maximal quotient of | C4×#63214, C22⋊#63214, C4⋊#63214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 18);