Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#13063443 |
| Sylow | C173 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#10621924 |
| commutator | C2×C173 | C2×C8 |
| Fitting | C23×C173 | C4 |
| socle | C22×C173 | C2×C4 |
| hypercenter | C23 | #10621924 |
| hypocenter | C173 | C22⋊C8 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ C23 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=d,d^2=e,b^a=bc,f^a=f^80,f^d=f^172364 conjugacy classes — view the full character table.
| maximal subgroup of | #26012334, #26012335, #26012336, … |
| maximal normal subgroup of | #26012334, #26012335, #26012336, … |
| maximal quotient of | #26012334, #26012336, D4⋊#13063443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 202);