Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C4 |
| direct product | C22×#14583615 |
| Fitting | C22×C4⋊Q8×C43 ⋊ C2 |
| Sylow | C43 ⋊ C22×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D43 |
| commutator, cosocle | C22×C43 | C26 |
| Frattini | C22 | C25×D43 |
| Fitting | C22×C4⋊Q8×C43 | C2 |
| socle | C24×C43 | C24 |
| hypercenter | C22×C4⋊Q8 | D43 |
| hypocenter | C43 | C22×#555 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊Q8 | |
8710 conjugacy classes of subgroups.
1276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 1076588);