Finite Group DatabasebetaFinite Group Databasebeta| order | 5816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D727 |
| Fitting | C4×C727 ⋊ C2 |
| derived, Sylow | C727 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D727 |
| commutator, hypocenter | C727 | C2×C4 |
| Frattini | C2 | C2×D727 |
| Fitting | C4×C727 | C2 |
| socle | C2×C727 | C22 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
1460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D727, #26042723, C2×C4×D727, … |
| maximal normal subgroup of | C8×D727, #26042723, C2×C4×D727, … |
| maximal quotient of | C4×Dic727, (C2×D727)⋊C4, Dic727⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5816, 7);