Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C22 |
| direct product | #471×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C79 |
| prime radical | AGL(1,ℤ/8)×C79 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×C4×C79 ◁ G | |
104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#471×C79, C79×#3067, C79×#3068, … |
| maximal normal subgroup of | C2×#471×C79, C79×#3067, C79×#3068, … |
| maximal quotient of | C79×#1665, C79×#1666, C79×#1671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 152);