Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#17984563 |
| Fitting | C23×C4×C277 ⋊ C2 |
| Sylow | C277 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D277 |
| commutator, cosocle | C2×C277 | C25 |
| Frattini | C2 | C24×D277 |
| Fitting | C23×C4×C277 | C2 |
| socle | C23×C277 | C23 |
| hypercenter | C23×C4 | D277 |
| hypocenter | C277 | C22×#41 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
4456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983078, #47983084, #47983093, … |
| maximal normal subgroup of | #47983078, #47983084, #47983093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1376);