Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C157 · Schur multiplier (H2) = C22 |
| direct product | C22⋊Q8×C157 |
| unambiguous semidirect product | C22⋊(Q8×C157) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C157 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C157 |
| prime radical | C23×C157 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C157 ◁ G | |
74 conjugacy classes of subgroups.
2198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #328×C157, #450×C157, #451×C157, … |
| maximal normal subgroup of | #328×C157, #450×C157, #451×C157, … |
| maximal quotient of | #380×C157, #385×C157, #387×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 29);