Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C43 · Schur multiplier (H2) = C23×C4 |
| direct product | C43×#8170 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | C2×D4 |
| commutator | C4 | C2×C4×C8×C43 |
| Frattini, cosocle | C2×C42 | C23×C43 |
| socle | C23×C43 | C2×C22⋊C4 |
| prime radical | C22×D4×C43 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ C43×C43 ◁ G | |
718 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, 1158);