Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of ((C5⋊D5)⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | H(3,𝔽5) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | ((C5⋊D5)⋊C5)⋊C2 |
| commutator, hypocenter | H(3,𝔽5) | C42 |
| Frattini, socle | C22×C5 | D52 |
| Fitting, prime radical, cosocle | C22×H(3,𝔽5) | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C22 | |
137 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=c,f^a=f^4,g^a=g^4,e^b=e^4,g^b=g^4,f^e=fg80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 109);