Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C37 ⋊ #476 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=df,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^36,e^c=ef271 conjugacy classes — view the full character table.
| maximal subgroup of | #476×D37, C2×#14557821, #18004380, … |
| maximal normal subgroup of | #476×D37, C2×#14557821, #18004380, … |
| maximal quotient of | #17994594, #17994855, #17994859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 837);