Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#19139520 |
| Fitting | C2×C43×#392 ⋊ C2 |
| Sylow | C43 ⋊ C2×#2539 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D43 |
| commutator, cosocle | C23×C43 | C25 |
| Frattini | C23 | C24×D43 |
| Fitting | C2×C43×#392 | C2 |
| socle | C24×C43 | C24 |
| hypercenter | C2×#392 | D43 |
| hypocenter | C43 | C2×#2539 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C2×#392 | |
5726 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 339597);