Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×C4⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C23 |
| Fitting | C52×C4⋊C4 | C2 |
| prime radical | C22×C5⋊D5 | C22 |
| hypercenter | C4⋊C4 | C5⋊D5 |
| hypocenter | C52 | C22⋊Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=de,c^a=cd,f^a=f^4,g^a=g^4,c^b=ce134 conjugacy classes — view the full character table.
| maximal subgroup of | #13100247, #13100339, #13100597, … |
| maximal normal subgroup of | #13100247, #13100339, #13100597, … |
| maximal quotient of | #13102518, #13102519, #13102520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 876);