Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊Q8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #461 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^36271 conjugacy classes — view the full character table.
| maximal subgroup of | #17993772, #17993774, #17993793, … |
| maximal normal subgroup of | #17993772, #17993774, #17993793, … |
| maximal quotient of | #17993968, #17993982, #17993992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 751);