Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#11764308 |
| unambiguous semidirect product | D277⋊(C23×C4) |
| Fitting, socle | C24×C277 ⋊ C4 |
| derived, Sylow | C277 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #11764308 |
| commutator, hypocenter | C277 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C277 | C4 |
| prime radical | C24×D277 | C2 |
| cosocle | D277 | C25 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C24 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
1168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1630);