Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #6053⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#6053⋊C2 |
| unambiguous semidirect product | #6053⋊(C2×C5) |
| Fitting, socle, Sylow | C53 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #6053⋊C2 |
| commutator | C5⋊D5 | C2×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C53 | M16 |
| prime radical | C5×D52 | C4 |
| cosocle | #1043 | C22×C5 |
| hypocenter | C52 | C5×M16 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C5 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
65 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 910);