Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C37 ⋊ #477 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=df,b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^36,e^c=ef,g^c=g^36379 conjugacy classes — view the full character table.
| maximal subgroup of | #17993718, #17993719, #17993724, … |
| maximal normal subgroup of | #17993718, #17993719, #17993724, … |
| maximal quotient of | #17994602, #17994853, #17995189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 845);