Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C37 ⋊ #340 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^36604 conjugacy classes — view the full character table.
| maximal subgroup of | #17992605, #17992606, #17992608, … |
| maximal normal subgroup of | #17992605, #17992606, #17992608, … |
| maximal quotient of | #17992431, #17992436, #17992455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 312);