Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C37 ⋊ C2 |
| Sylow | C37 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^6,37|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^36,d^b=df,e^b=ef,d^c=df322 conjugacy classes — view the full character table.
| maximal subgroup of | #17996578, #17996590, #17996600, … |
| maximal normal subgroup of | #17996578, #17996590, #17996600, … |
| maximal quotient of | #17993514, #17993519, #17993542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 717);