Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C79 · Schur multiplier (H2) = C2×C4 |
| direct product | #486×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C79 |
| prime radical | #127×C79 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ G | |
118 conjugacy classes of subgroups.
1738 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#1625, C79×#1626, C79×#1627, … |
| maximal normal subgroup of | C79×#1625, C79×#1626, C79×#1627, … |
| maximal quotient of | C79×#1834, C79×#1934, C79×#1957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 167);