Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×#14583829 |
| derived, Sylow | C173 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #10621924 |
| commutator, hypocenter | C173 | C8×C16 |
| Frattini | C42 | C2×#10621924 |
| Fitting | C4×C8×C173 | C4 |
| socle, prime radical | C22×C173 | C4×C8 |
| cosocle | C4×#13063436 | C22 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C4×C8 | |
104 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, 19420);