Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C79 · Schur multiplier (H2) = C25 |
| direct product | #568×C79 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C79 | C24 |
| commutator | C2 | C23×C4×C79 |
| Frattini, cosocle | C4 | C24×C79 |
| socle | C2×C79 | C23×C4 |
| prime radical | C2×#41×C79 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C79 ◁ G | |
258 conjugacy classes of subgroups.
2686 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#1858, C79×#1861, C79×#1868, … |
| maximal normal subgroup of | C79×#1858, C79×#1861, C79×#1868, … |
| maximal quotient of | C79×#2873, C79×#2875, C79×#2879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 249);