Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#64436 |
| Sylow | C37 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^36,c^b=ce388 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊C8×D37, C2×Q8⋊#64436, #17992977, … |
| maximal normal subgroup of | Q8⋊C8×D37, C2×Q8⋊#64436, #17992977, … |
| maximal quotient of | #17992419, #17992422, #17992437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 280);