Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C37 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^36,d^b=df,g^c=g^36274 conjugacy classes — view the full character table.
| maximal subgroup of | #17996495, #17996497, #442×D37, … |
| maximal normal subgroup of | #17996495, #17996497, #442×D37, … |
| maximal quotient of | #17993420, #17993461, #17993510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 661);