Finite Group DatabasebetaFinite Group Databasebeta| order | 5216 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C163 · Schur multiplier (H2) = C26 |
| direct product | C22×D4×C163 |
| unambiguous semidirect product | C4⋊(C23×C163) |
| unambiguous semidirect product | C22⋊(C23×C163) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C163 | C22 |
| commutator, Frattini, cosocle | C2 | C24×C163 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C163 ◁ G | |
236 conjugacy classes of subgroups.
3260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #386×C163, #390×C163, #392×C163, … |
| maximal normal subgroup of | #386×C163, #390×C163, #392×C163, … |
| maximal quotient of | C22×C22⋊C4×C163, C22×C4⋊C4×C163, C2×C4×D4×C163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5216, 46);