Finite Group DatabasebetaFinite Group Databasebeta| order | 28556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊D11)⋊D59 |
| unambiguous semidirect product | D649⋊D11 |
| Fitting, socle, derived, Hall | C112×C59 ⋊ C22 |
| Sylow | C112 ⋊ C2×D59 |
| Sylow | C59 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C59 | C22 |
| LCS | G ▷ C112×C59 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1298 |
Polycyclic presentation:
2^2,11^2,59|c^a=c^10,e^a=e^58,c^b=c^10,d^b=d^101847 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28556, 22);