Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C157 · Schur multiplier (H2) = C4 |
| direct product | #490×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C157 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C157 |
| prime radical | #127×C157 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C157 ◁ C42×C157 ◁ G | |
110 conjugacy classes of subgroups.
2512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1355×C157, #1412×C157, #1656×C157, … |
| maximal normal subgroup of | #1355×C157, #1412×C157, #1656×C157, … |
| maximal quotient of | #1836×C157, #1936×C157, #1961×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 171);