Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C157 · Schur multiplier (H2) = C1 |
| direct product | #108×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C157 | D4 |
| commutator | C4 | C2×C4×C157 |
| Frattini, cosocle | C2×C4 | C22×C157 |
| socle | C2×C157 | C4⋊C4 |
| prime radical | C22×C157 | Q8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C157 ◁ C2×C4×C157 ◁ G | |
30 conjugacy classes of subgroups.
2198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #359×C157, #361×C157, #362×C157, … |
| maximal normal subgroup of | #359×C157, #361×C157, #362×C157, … |
| maximal quotient of | #334×C157, #335×C157, #341×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 15);