Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#64438 |
| 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^31,c^b=ce,g^d=g^36118 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#64438, D37⋊(Q8⋊C8), #18009887, … |
| maximal normal subgroup of | C2×Q8⋊#64438, D37⋊(Q8⋊C8), #18009887, … |
| maximal quotient of | #18009414, #18009416, #18009432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1398);