Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C37 ⋊ #329 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^36,c^b=cf,d^b=def271 conjugacy classes — view the full character table.
| maximal subgroup of | #17992743, #17992744, #17992746, … |
| maximal normal subgroup of | #17992743, #17992744, #17992746, … |
| maximal quotient of | #17992417, #17992422, #17992477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 289);