Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C23 |
| Fitting, prime radical | C2×C52×D4 | C2 |
| hypercenter | C2×D4 | C5⋊D5 |
| hypocenter | C52 | #124 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=d,c^a=cde,f^a=f^4,g^a=g^4,c^b=cd134 conjugacy classes — view the full character table.
| maximal subgroup of | #13099351, #13099507, #13100299, … |
| maximal normal subgroup of | #13099351, #13099507, #13100299, … |
| maximal quotient of | #13102808, #13102810, #13102816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 915);