Finite Group DatabasebetaFinite Group Databasebeta| order | 22688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D709⋊C8 |
| unambiguous semidirect product | D709⋊(C2×C8) |
| derived, Sylow | C709 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #15667778 |
| commutator, hypocenter | C709 | C22×C8 |
| Frattini | C2 | C22×#15667778 |
| Fitting | C2×C4×C709 | C4 |
| socle | C22×C709 | C2×C4 |
| prime radical | C22×D709 | C4 |
| cosocle | Dic709 | C23 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11344 |
1448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22688, 229);