Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C37 ⋊ #487 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^36,g^b=g^36,g^c=g^36274 conjugacy classes — view the full character table.
| maximal subgroup of | #17993747, #17993748, #17993754, … |
| maximal normal subgroup of | #17993747, #17993748, #17993754, … |
| maximal quotient of | #17994723, #17995271, #17995397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 901);