Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C43 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×C43×#342 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | C22⋊C4 |
| commutator | C22 | C43×C43 |
| Frattini, cosocle | C25 | C23×C43 |
| socle | C23×C43 | C2×C22⋊C4 |
| prime radical | C25×C43 | C23 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ C24×C4×C43 ◁ G | |
1482 conjugacy classes of subgroups.
3784 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 3696);