Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×#63242 |
| derived, Sylow | C17 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #595 |
| commutator, hypocenter | C17 | C23×C8 |
| Frattini | C2 | C23×#595 |
| Fitting | C22×C4×C17 | C4 |
| socle | C23×C17 | C2×C4 |
| prime radical | C23×D17 | C4 |
| cosocle | Dic17 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C4 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11763674, #14544445, #14544451, … |
| maximal normal subgroup of | C2×#11763674, #14544445, #14544451, … |
| maximal quotient of | C22×C4×#3624, C2×C4×#63242, C2×#11763777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1620);