Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22⋊C4×C37 ⋊ C4 |
| Sylow | C37 ⋊ #352 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^6,37|a^2=d,b^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^31,d^b=de,g^b=g^36,d^c=df,g^d=g^36103 conjugacy classes — view the full character table.
| maximal subgroup of | D37⋊#352, C2×#14558436, #18010848, … |
| maximal normal subgroup of | D37⋊#352, C2×#14558436, #18010848, … |
| maximal quotient of | #18009523, #18009540, #18009577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1452);