Finite Group DatabasebetaFinite Group Databasebeta| order | 5056 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C79 · Schur multiplier (H2) = C23 |
| direct product | C8×D4×C79 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C79 | C22 |
| commutator | C2 | C22×C8×C79 |
| Frattini, cosocle | C2×C4 | C23×C79 |
| socle | C22×C79 | C22×C4 |
| prime radical | C2×D4×C79 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C79 ◁ G | |
134 conjugacy classes of subgroups.
3160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×D4⋊C16, C8×D8×C79, C8×SD16×C79, … |
| maximal normal subgroup of | C79×D4⋊C16, C8×D8×C79, C8×SD16×C79, … |
| maximal quotient of | C8×D8×C79, C8×SD16×C79, C8×Q16×C79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5056, 115);