Finite Group DatabasebetaFinite Group Databasebeta| order | 5968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C373 ⋊ C2 |
| Sylow | C373 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D373 |
| commutator, socle | C2×C373 | C23 |
| Fitting | D4×C373 | C2 |
| hypercenter | D4 | D373 |
| hypocenter | C373 | #41 |
| LCS | G ▷ C2×C373 ▷ C373 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,373|c^2=d,b^a=bd,e^c=e^372940 conjugacy classes — view the full character table.
| maximal subgroup of | #26045811, #26045813, #26045816, … |
| maximal normal subgroup of | #26045811, #26045813, #26045816, … |
| maximal quotient of | #26045748, #26045750, #26045752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5968, 39);