Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C79 · Schur multiplier (H2) = C2 |
| direct product | #329×C79 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C22⋊C4 |
| commutator | C2×C4 | C2×C4×C79 |
| Frattini, cosocle | C42 | C22×C79 |
| prime radical | C2×D4×C79 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ G | |
70 conjugacy classes of subgroups.
1501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#1403, C79×#1404, C2×#329×C79, … |
| maximal normal subgroup of | C79×#1403, C79×#1404, C2×#329×C79, … |
| maximal quotient of | C79×#1270, C79×#1272, C79×#1295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 10);