Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | D43×#2639 |
| Fitting | C43×#2639 ⋊ C2 |
| Sylow | C43 ⋊ C2×#2639 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D43 |
| commutator, socle, cosocle | C23×C43 | C25 |
| Fitting | C43×#2639 | C2 |
| prime radical | C2×#121×D43 | C2 |
| hypercenter | #2639 | D43 |
| hypocenter | C43 | C2×#2639 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #2639 | |
3326 conjugacy classes of subgroups.
736 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 336000);