Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6037 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#6039 |
| Sylow | C52 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D52 |
| commutator, cosocle | C2×C52 | C24 |
| Frattini | C2 | C22×D52 |
| Fitting, socle, prime radical | C23×C52 | C22 |
| hypocenter | C52 | C22×Q8 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 | |
366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #13101570, #13101571, #13101572, … |
| maximal normal subgroup of | #13101570, #13101571, #13101572, … |
| maximal quotient of | C2×#11716988, C2×#11716991, C2×C4×#6039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1151);