Finite Group DatabasebetaFinite Group Databasebeta| order | 5968 |
| automorphism | Aut(G) order 4440192 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2984 |
| Fitting | C8×C373 ⋊ C2 |
| Sylow | C373 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1492 |
| commutator | C4×C373 | C22 |
| Frattini | C4 | C2×D373 |
| Fitting | C8×C373 | C2 |
| socle | C2×C373 | D4 |
| hypercenter | C8 | D373 |
| hypocenter | C373 | D8 |
| LCS | G ▷ C4×C373 ▷ C2×C373 ▷ C373 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,373|c^2=d,b^a=bc,c^a=cd,e^a=e^372,c^b=cd,e^b=e^3721495 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26045733, D5968, #26045735, … |
| maximal normal subgroup of | #26045733, D5968, #26045735, … |
| maximal quotient of | #26045714, #26045726, D5968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5968, 26);