Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#13063443 |
| derived, Sylow | C173 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10621924 |
| commutator, hypocenter | C173 | C22×C8 |
| Frattini | C2 | C22×#10621924 |
| Fitting, socle | C23×C173 | C4 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C23 | |
76 conjugacy classes of subgroups.
376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 228);