Finite Group DatabasebetaFinite Group Databasebeta| order | 5072 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#11929639 |
| Fitting | C4×C317 ⋊ C4 |
| derived, Sylow | C317 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #11929639 |
| commutator, hypocenter | C317 | C42 |
| Frattini | C2 | C2×#11929639 |
| Fitting | C4×C317 | C4 |
| socle | C2×C317 | C2×C4 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5072, 44);