Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C24 |
| direct product | #554×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C79 |
| prime radical | C2×D4×C79 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ G | |
228 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1975 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#1622, C79×#1632, C79×#1643, … |
| maximal normal subgroup of | C79×#1622, C79×#1632, C79×#1643, … |
| maximal quotient of | C79×#2345, D4×C4⋊C4×C79, C79×#2349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 235);