Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C52×C8 ⋊ C4 |
| Sylow | C52 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#1042 |
| commutator, socle | C2×C52 | C42 |
| Fitting | C52×C8 | C4 |
| prime radical | C2×C5×D5 | C2×C4 |
| cosocle | C4×C5×D5 | C22 |
| hypercenter | C8 | #1042 |
| hypocenter | C52 | #97 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C8 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^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 | #13099716, #13099717, #13100129, … |
| maximal normal subgroup of | #13099716, #13099717, #13100129, … |
| maximal quotient of | #13100129, #13100130, #13100163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 494);