Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5⋊#1042 |
| commutator, Fitting, socle | C2×C53 | C2×C4 |
| prime radical, cosocle | C2×C5×C5⋊D5 | C22 |
| hypocenter | C53 | C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^4,e^b=e^4,e^c=e^4,f^c=f^486 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87832, #72259195, #72259199 |
| maximal normal subgroup of | D5×#87832, #72259195, #72259199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 671);