Finite Group DatabasebetaFinite Group Databasebeta| order | 5816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C727 · Schur multiplier (H2) = C2 |
| direct product | D4×C727 |
| unambiguous semidirect product | C4⋊(C2×C727) |
| unambiguous semidirect product | C22⋊(C2×C727) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C727 | C22 |
| commutator, Frattini | C2 | C22×C727 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C727 ◁ G | |
16 conjugacy classes of subgroups.
3635 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×C727, SD16×C727, C2×D4×C727, … |
| maximal normal subgroup of | D8×C727, SD16×C727, C2×D4×C727, … |
| maximal quotient of | C22⋊C4×C727, C4⋊C4×C727, D8×C727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5816, 3);