Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C22×SD16×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | D4 |
| commutator, Frattini, cosocle | C4 | C24×C79 |
| prime radical | C22×D4×C79 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C22×C4×C79 ◁ G | |
298 conjugacy classes of subgroups.
2212 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#1877, C79×#1880, C79×#1968, … |
| maximal normal subgroup of | C79×#1877, C79×#1880, C79×#1968, … |
| maximal quotient of | C22×#102×C79, C22×#103×C79, C22×#106×C79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 251);