Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×D277 |
| Fitting | 2−1+4×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D277 |
| commutator, socle, cosocle | C2×C277 | C25 |
| Fitting | 2−1+4×C277 | C2 |
| hypercenter | 2−1+4 | D277 |
| hypocenter | C277 | C2×2−1+4 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
2380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1381);