Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Sylow | C52 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C5⋊D5 |
| commutator, socle, prime radical, cosocle | C22×C52 | C23 |
| Fitting | C2×C52×Q8 | C2 |
| hypercenter | C2×Q8 | C5⋊D5 |
| hypocenter | C52 | C4⋊Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=d,c^2=d,c^a=ce,f^a=f^4,g^a=g^4,c^b=cd134 conjugacy classes — view the full character table.
| maximal subgroup of | #13099355, #13099512, #13100307, … |
| maximal normal subgroup of | #13099355, #13099512, #13100307, … |
| maximal quotient of | #13102830, #13102832, #13102833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 923);