Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C43 · Schur multiplier (H2) = C4 |
| direct product | C43×#7733 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C43 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C43 |
| Frattini, cosocle | C2×C42 | C23×C43 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C43×C43 ◁ G | |
366 conjugacy classes of subgroups.
1978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 721);