Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C37 ⋊ #559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D37 |
| commutator, socle, cosocle | C22×C37 | C24 |
| Fitting, prime radical | #127×C37 | C2 |
| hypercenter | #127 | D37 |
| hypocenter | C37 | #559 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #127 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=ef,c^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^36,d^b=de,g^b=g^36277 conjugacy classes — view the full character table.
| maximal subgroup of | #17993653, #17993656, #17993715, … |
| maximal normal subgroup of | #17993653, #17993656, #17993715, … |
| maximal quotient of | #17997555, #17997568, #17997661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1285);