Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#13063436 |
| derived, Sylow | C173 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D173 |
| commutator, hypocenter | C173 | C24×C8 |
| Frattini | C4 | C24×D173 |
| Fitting | C24×C4×C173 | C2 |
| socle, prime radical | C25×C173 | C4 |
| cosocle | C4×C173 | C25 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22144 |
5632 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19209);