Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #63219 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D136 |
| Fitting | C22×C8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D68 |
| commutator, cosocle | C4×C17 | C24 |
| Frattini | C4 | C23×D17 |
| Fitting | C22×C8×C17 | C2 |
| socle | C23×C17 | D4 |
| hypercenter | C22×C8 | D17 |
| hypocenter | C17 | C22×D8 |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14529131, #14529133, #14529648, … |
| maximal normal subgroup of | #14529131, #14529133, #14529648, … |
| maximal quotient of | C22×#10587492, C22×#10587489, C2×C4×D136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1319);