Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #107 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #6037 |
| commutator | C4×C52 | C2×C4 |
| Frattini, hypercenter | C2×C4 | D52 |
| Fitting, cosocle | C2×C4×C52 | C22 |
| socle, prime radical | C22×C52 | D4 |
| hypocenter | C52 | #107 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=c,d^2=e,b^a=bd,d^a=de,g^a=g^4,d^b=de,f^b=f^486 conjugacy classes — view the full character table.
| maximal subgroup of | #13099993, #13099994, #13100000, … |
| maximal normal subgroup of | #13099993, #13099994, #13100000, … |
| maximal quotient of | #13099270, #13099310, #13099312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 276);