Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C43 · Schur multiplier (H2) = C22 |
| direct product | C43×#13638 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C43 | #367 |
| commutator | C16 | C22×C4×C43 |
| Frattini, cosocle | C2×C16 | C23×C43 |
| socle | C2×C43 | C2×#367 |
| prime radical | C23×C43 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C43 ◁ C22×C4×C43 ◁ C22×C8×C43 ◁ C22×C16×C43 ◁ G | |
182 conjugacy classes of subgroups.
2236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 6626);