Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #1042⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #1042⋊D5 |
| Fitting, socle, derived, Sylow | C53 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53 | C2×C4 |
| prime radical | D5×C5⋊D5 | C2 |
| cosocle | C52×D5 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
Polycyclic presentation:
2^3,5^3|a^2=c,b^2=c,d^a=d^3,f^a=f^4,d^b=d^2,e^b=e^4,d^c=d^446 conjugacy classes — view the full character table.
| maximal subgroup of | #14522936, #14522937, #14522942, … |
| maximal normal subgroup of | #14522936, #14522937, #14522942, … |
| maximal quotient of | #14522735, #14522736, #14522737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 177);