Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #11758788 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C53 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11758788 |
| commutator, hypocenter | C53 | C42 |
| Fitting, socle | C2×C53 | C2×C4 |
| prime radical, cosocle | C2×C5×C5⋊D5 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=c,e^a=e^4,g^a=g^4,e^b=e^2,f^b=f^2,e^c=e^4,f^c=f^468 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87830, #72259205, #72259208, … |
| maximal normal subgroup of | D5×#87830, #72259205, #72259208, … |
| maximal quotient of | C2×#14522711 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 674);