Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#13092981 |
| Fitting | C22×#41×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#535 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D23 |
| commutator, cosocle | C22×C23 | C25 |
| Frattini | C22 | C24×D23 |
| Fitting | C22×#41×C23 | C2 |
| socle | C23×C23 | C24 |
| hypercenter | C22×#41 | D23 |
| hypocenter | C23 | C2×#535 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
1896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 17816);