Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#10596927 |
| Sylow | C37 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^31,g^d=g^36184 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#10596927, #18009547, #18009548, … |
| maximal normal subgroup of | D4⋊#10596927, #18009547, #18009548, … |
| maximal quotient of | #18009618, #18009625, #18009634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1469);