Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C7×C64 (order 5376) · Inn(G) = C1 · Out(G) = C22×C3×C7×C64 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C11008 |
| abelian | C43×C256 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C2×C43 |
| socle, prime radical | C2×C43 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18 conjugacy classes of subgroups.
11008 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic11008, D22016 |
| maximal subgroup of | C43×C512, C2×C43×C256, D11008, … |
| maximal normal subgroup of | C43×C512, C2×C43×C256, D11008, … |
| maximal quotient of | C43×C512, C2×C43×C256 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 1);