Finite Group DatabasebetaFinite Group Databasebeta| order | 5968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D373 |
| Fitting | Q8×C373 ⋊ C2 |
| Sylow | C373 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D373 |
| commutator, socle | C2×C373 | C23 |
| Fitting | Q8×C373 | C2 |
| hypercenter | Q8 | D373 |
| hypocenter | C373 | C2×Q8 |
| LCS | G ▷ C2×C373 ▷ C373 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
940 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D373, Q16×D373, #26045821, … |
| maximal normal subgroup of | SD16×D373, Q16×D373, #26045821, … |
| maximal quotient of | C4⋊C4×D373, #26045757, Q8×Dic373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5968, 37);