Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽5) ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2×C5 | #6057 |
| commutator | #6953 | C2×C4 |
| Fitting | C2×H(3,𝔽5) | Q8 |
| prime radical, cosocle | C2×#6953 | C22 |
| hypocenter | H(3,𝔽5) | C4⋊C4 |
| LCS | G ▷ #6953 ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C2×C5 | |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=c,b^a=bcd,e^a=e^2,f^a=f^3g^3,e^b=fg^4,f^b=e^4g,e^c=e^4,f^c=f^4g^2,f^e=fg56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 273);