Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | D43×#3509 |
| Fitting | C43×#3509 ⋊ C2 |
| Sylow | C43 ⋊ C2×#3509 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D43 |
| commutator, socle, cosocle | C22×C43 | C26 |
| Fitting | C43×#3509 | C2 |
| prime radical | C2×#41×D43 | C22 |
| hypercenter | #3509 | D43 |
| hypocenter | C43 | C2×#3509 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #3509 | |
7022 conjugacy classes of subgroups.
1012 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 1078002);