Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C43 · Schur multiplier (H2) = C23 |
| direct product | C43×#7471 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C43 | D16 |
| commutator | C16 | C42×C43 |
| Frattini, cosocle | C22×C16 | C22×C43 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ C22×C4×C43 ◁ C22×C8×C43 ◁ C22×C16×C43 ◁ G | |
190 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 459);