Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D52 |
| commutator, socle, cosocle | C2×C52 | C24 |
| Fitting | C52×Q8 | C22 |
| hypercenter | Q8 | D52 |
| hypocenter | C52 | 2−1+4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|c^2=e,d^2=e,b^a=be,g^a=g^4,f^b=f^4,d^c=de77 conjugacy classes — view the full character table.
| maximal subgroup of | #13104345, #13104346, #13105839, … |
| maximal normal subgroup of | #13104345, #13104346, #13105839, … |
| maximal quotient of | #13105404, #13105406, #13105415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1140);