Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C37 ⋊ C4 |
| Sylow | C37 ⋊ #327 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,c^2=f,b^a=bc,c^a=ce,g^a=g^31,c^b=cf,d^b=def,g^b=g^36,g^d=g^36109 conjugacy classes — view the full character table.
| maximal subgroup of | D37⋊#327, C2×#14558385, #18009969, … |
| maximal normal subgroup of | D37⋊#327, C2×#14558385, #18009969, … |
| maximal quotient of | #18009413, #18009414, #18009469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1401);