Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#63241 |
| derived, Sylow | C17 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #3633 |
| commutator, hypocenter | C17 | C2×C16 |
| Frattini | C2 | C2×#3633 |
| Fitting, socle, prime radical | C22×C17 | C8 |
| cosocle | #3624 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#63241, #11763903, C22⋊#63241, … |
| maximal normal subgroup of | C4×#63241, #11763903, C22⋊#63241, … |
| maximal quotient of | C4×#63241, C22⋊#63241, C4⋊#63241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 205);