Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Fitting | C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ D16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #87809 |
| commutator, cosocle | C52×C8 | C22 |
| Frattini | C8 | C2×C5⋊D5 |
| Fitting | C52×D8 | C2 |
| socle | C2×C52 | D8 |
| hypercenter | D8 | C5⋊D5 |
| hypocenter | C52 | D16 |
| LCS | G ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^4,g^a=g^4,c^b=cd,d^b=de95 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3958, #13101205, #13101214, … |
| maximal normal subgroup of | D5×#3958, #13101205, #13101214, … |
| maximal quotient of | #13099523, #13099525, #13099553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 352);