Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D52 |
| commutator, socle, cosocle | C2×C52 | C24 |
| Fitting | C2×C4×C52 | C22 |
| hypercenter | C2×C4 | D52 |
| hypocenter | C52 | 2−1+4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=e,d^2=e,d^a=de,g^a=g^4,c^b=ce,f^b=f^489 conjugacy classes — view the full character table.
| maximal subgroup of | #13100582, #13100583, #13101198, … |
| maximal normal subgroup of | #13100582, #13100583, #13101198, … |
| maximal quotient of | #13104939, #13104947, #13104949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1122);