Finite Group DatabasebetaFinite Group Databasebeta| order | 22376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D2797 |
| Fitting | C22×C2797 ⋊ C2 |
| Sylow | C2797 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D2797 |
| commutator, socle, cosocle | C2×C2797 | C22 |
| Fitting | C22×C2797 | C2 |
| hypercenter | C22 | D2797 |
| hypocenter | C2797 | D4 |
| LCS | G ▷ C2×C2797 ▷ C2797 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11188 |
Polycyclic presentation:
2^3,2797|b^a=bc,d^b=d^27965597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22376, 9);