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.
| 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,c^b=cef,d^b=df,e^b=ef,g^b=g^36268 conjugacy classes — view the full character table.
| maximal subgroup of | #362×D37, C2×#14557348, #17996342, … |
| maximal normal subgroup of | #362×D37, C2×#14557348, #17996342, … |
| maximal quotient of | #17992565, #17992613, #17992644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 364);