Finite Group DatabasebetaFinite Group Databasebeta| order | 20408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D2551 |
| Fitting | C22×C2551 ⋊ C2 |
| Sylow | C2551 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D2551 |
| commutator, socle, cosocle | C2×C2551 | C22 |
| Fitting | C22×C2551 | C2 |
| hypercenter | C22 | D2551 |
| hypocenter | C2551 | D4 |
| LCS | G ▷ C2×C2551 ▷ C2551 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10204 |
Polycyclic presentation:
2^3,2551|b^a=bc,d^b=d^25505105 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20408, 9);