Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of (((C5⋊D5)⋊C5)⋊C2)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×(((C5⋊D5)⋊C5)⋊C2)⋊C2 |
| unambiguous semidirect product | (((C5⋊D5)⋊C5)⋊C2)⋊C22 |
| Fitting | C2×H(3,𝔽5) ⋊ D4 |
| Sylow | H(3,𝔽5) ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (((C5⋊D5)⋊C5)⋊C2)⋊C2 |
| commutator, cosocle | #6953 | C23 |
| Frattini | C5 | C2×D52⋊C2 |
| Fitting | C2×H(3,𝔽5) | D4 |
| socle | C2×C5 | D52⋊C2 |
| hypocenter | H(3,𝔽5) | C2×D4 |
| LCS | G ▷ #6953 ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C2 | |
161 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 482);