Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C157 · Schur multiplier (H2) = C22 |
| direct product | #354×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C157 | #99 |
| commutator | C2×C4 | C2×C4×C157 |
| Frattini, cosocle | C2×D4 | C22×C157 |
| prime radical | C2×D4×C157 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C157 ◁ C22×C157 ◁ C2×D4×C157 ◁ G | |
70 conjugacy classes of subgroups.
2041 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1404×C157, #1406×C157, #1407×C157, … |
| maximal normal subgroup of | #1404×C157, #1406×C157, #1407×C157, … |
| maximal quotient of | #1319×C157, #1324×C157, #1344×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 35);