Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#1042 |
| commutator, socle | C2×C52 | C2×C8 |
| Fitting | C52×C8 | C4 |
| prime radical | C2×C5×D5 | C8 |
| cosocle | C5×#168 | C22 |
| hypercenter | C8 | #1042 |
| hypocenter | C52 | M32 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,c^2=d,d^2=e,b^a=be,f^a=f^4,g^a=g^3,g^c=g^492 conjugacy classes — view the full character table.
| maximal subgroup of | #13099714, #13099715, #13099726, … |
| maximal normal subgroup of | #13099714, #13099715, #13099726, … |
| maximal quotient of | #13100170, #13100171, #13100172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 492);