Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4×C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #488 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^36598 conjugacy classes — view the full character table.
| maximal subgroup of | #488×D37, C2×#14557888, #18004917, … |
| maximal normal subgroup of | #488×D37, C2×#14557888, #18004917, … |
| maximal quotient of | #17994727, #17995272, #17995279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 904);