Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C157 · Schur multiplier (H2) = C210 |
| direct product | C23×D4×C157 |
| unambiguous semidirect product | C4⋊(C24×C157) |
| unambiguous semidirect product | C22⋊(C24×C157) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C157 | C22 |
| commutator, Frattini, cosocle | C2 | C25×C157 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C157 ◁ G | |
1362 conjugacy classes of subgroups.
6280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1438×C157, #1781×C157, #1783×C157, … |
| maximal normal subgroup of | #1438×C157, #1781×C157, #1783×C157, … |
| maximal quotient of | C23×C22⋊C4×C157, C23×C4⋊C4×C157, C22×C4×D4×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 261);