Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C37 ⋊ #362 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^31,c^b=cef,d^b=df,e^b=ef,g^d=g^3679 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14558452, D37⋊#362, #18010923, … |
| maximal normal subgroup of | C2×#14558452, D37⋊#362, #18010923, … |
| maximal quotient of | #18009556, #18009557, #18009588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1468);