Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #64438⋊C8 |
| Sylow | C37 ⋊ #322 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^a=g^31,g^c=g^36184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64438⋊C8, #18009792, C8×#10596957, … |
| maximal normal subgroup of | C2×#64438⋊C8, #18009792, C8×#10596957, … |
| maximal quotient of | #18009418, #64438⋊C16, #18009514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1391);