Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #92539 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#92539 |
| Fitting | C2×H(3,𝔽5) ⋊ C4 |
| derived, Sylow | H(3,𝔽5) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C5 | #1044 |
| commutator, hypocenter | H(3,𝔽5) | C2×C4 |
| Frattini | C5 | C2×#1044 |
| Fitting | C2×H(3,𝔽5) | C4 |
| prime radical | C2×#6953 | C2 |
| cosocle | #6953 | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C2×C5 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 104);