Finite Group DatabasebetaFinite Group Databasebeta| order | 5816 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C727⋊C8 |
| derived, Sylow | C727 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D727 |
| commutator, hypocenter | C727 | C8 |
| Fitting | C4×C727 | C2 |
| socle | C2×C727 | C4 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,727|a^2=b,b^2=c,d^a=d^7261460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D727, C2×C727⋊C8, #26042723, … |
| maximal normal subgroup of | C8×D727, C2×C727⋊C8, #26042723, … |
| maximal quotient of | C727⋊C16, C2×C727⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5816, 6);