Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #87877 |
| commutator, cosocle | C4×C52 | C23 |
| Frattini | C4 | C2×D52 |
| Fitting | C52×C8 | C22 |
| socle | C2×C52 | C2×D4 |
| hypercenter | C8 | D52 |
| hypocenter | C52 | #135 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,g^a=g^4,c^b=cd,d^b=de,f^b=f^474 conjugacy classes — view the full character table.
| maximal subgroup of | #13099950, #13099951, #13103871, … |
| maximal normal subgroup of | #13099950, #13099951, #13103871, … |
| maximal quotient of | #13100876, #13100877, #13100926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 586);