Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C25 ⋊ C2 |
| Sylow | C25 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D25 |
| commutator, cosocle | C2×C25 | C24 |
| Frattini, socle | C2×C5 | C23×D5 |
| Fitting | #41×C25 | C2 |
| hypercenter | #41 | D25 |
| hypocenter | C25 | 2−1+4 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ #41 | |
219 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=e,d^2=e,f^5=g,d^a=de,f^a=f^4g^4,g^a=g^4,c^b=ce137 conjugacy classes — view the full character table.
| maximal subgroup of | #13098101, #13098102, #13098476, … |
| maximal normal subgroup of | #13098101, #13098102, #13098476, … |
| maximal quotient of | #13098839, #13098841, #13098843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 228);