Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | C37⋊#564 |
| Sylow | C37 ⋊ #564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, prime radical, cosocle | C22×C37 | C24 |
| Fitting | #125×C37 | C2 |
| hypercenter | #125 | D37 |
| hypocenter | C37 | #564 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #125 | |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=e,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^d=g^36271 conjugacy classes — view the full character table.
| maximal subgroup of | #17993897, #17993899, #17993922, … |
| maximal normal subgroup of | #17993897, #17993899, #17993922, … |
| maximal quotient of | #17997778, #17997779, #17997780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1304);