Finite Group DatabasebetaFinite Group Databasebeta| order | 17768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D2221 |
| Fitting | C22×C2221 ⋊ C2 |
| Sylow | C2221 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D2221 |
| commutator, socle, cosocle | C2×C2221 | C22 |
| Fitting | C22×C2221 | C2 |
| hypercenter | C22 | D2221 |
| hypocenter | C2221 | D4 |
| LCS | G ▷ C2×C2221 ▷ C2221 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8884 |
Polycyclic presentation:
2^3,2221|b^a=bc,d^b=d^22204445 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D2221, C2×C22⋊D2221, #48001106, … |
| maximal normal subgroup of | D4×D2221, C2×C22⋊D2221, #48001106, … |
| maximal quotient of | #48001084, C22⋊Dic2221, #48001086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17768, 9);