Finite Group DatabasebetaFinite Group Databasebeta| order | 26944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#16809890 |
| derived, Sylow | C421 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D421 |
| commutator, hypocenter | C421 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D421 |
| Fitting | C2×C42×C421 | C2 |
| socle, prime radical | C23×C421 | C2×C4 |
| cosocle | C2×C4×C421 | C23 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26944 |
6784 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26944, 495);