Finite Group DatabasebetaFinite Group Databasebeta| order | 5968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#15688412 |
| derived, Sylow | C373 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D373 |
| commutator, hypocenter | C373 | C2×C8 |
| Frattini | C4 | C2×D373 |
| Fitting | C2×C4×C373 | C2 |
| socle | C22×C373 | C4 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
1504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic373, C4×#15688412, #26045702, … |
| maximal normal subgroup of | C8×Dic373, C4×#15688412, #26045702, … |
| maximal quotient of | C4×#15688412, C22⋊#15688412, C4⋊#15688412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5968, 22);