Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#14583829 |
| derived, Sylow | C173 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #10621924 |
| commutator, hypocenter | C173 | C23×C16 |
| Frattini | C4 | C23×#10621924 |
| Fitting | C23×C4×C173 | C4 |
| socle, prime radical | C24×C173 | C8 |
| cosocle | #13063436 | C24 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C23×C4 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22144 |
1504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 21469);