Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C37 ⋊ C2 |
| Sylow | C37 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^36,c^b=ce,e^b=ef,g^b=g^36598 conjugacy classes — view the full character table.
| maximal subgroup of | #359×D37, C2×#14557341, #17996322, … |
| maximal normal subgroup of | #359×D37, C2×#14557341, #17996322, … |
| maximal quotient of | #17992558, #17992561, #17992612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 357);