Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C25 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D25 |
| commutator, cosocle | C22×C25 | C23 |
| Frattini, socle, prime radical | C22×C5 | C22×D5 |
| Fitting | C2×Q8×C25 | C2 |
| hypercenter | C2×Q8 | D25 |
| hypocenter | C25 | C4⋊Q8 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=d,c^2=d,f^5=g,c^a=ce,f^a=f^4g^4,g^a=g^4,c^b=cd134 conjugacy classes — view the full character table.
| maximal subgroup of | #13097683, #13097915, #13097916, … |
| maximal normal subgroup of | #13097683, #13097915, #13097916, … |
| maximal quotient of | #13098247, #13098249, #13098250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 165);