Finite Group DatabasebetaFinite Group Databasebeta| order | 22336 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#14584102 |
| derived, Sylow | C349 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #13063703 |
| commutator, hypocenter | C349 | C23×C8 |
| Frattini | C2 | C23×#13063703 |
| Fitting, socle, prime radical | C24×C349 | C4 |
| cosocle | Dic349 | C24 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C24 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22336 |
1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22336, 1619);