Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C157 · Schur multiplier (H2) = C2 |
| direct product | D16×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C157 | D8 |
| commutator, Frattini, cosocle | C8 | C22×C157 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C157 ◁ C4×C157 ◁ C8×C157 ◁ G | |
28 conjugacy classes of subgroups.
1727 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×C157, SD64×C157, C2×D16×C157, … |
| maximal normal subgroup of | D32×C157, SD64×C157, C2×D16×C157, … |
| maximal quotient of | #357×C157, #366×C157, D32×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 18);