Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6037 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#6039 |
| Sylow | C52 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D52 |
| commutator | C2×C52 | C22×C4 |
| Frattini | C22 | C2×D52 |
| Fitting | C2×C4×C52 | C22 |
| socle, prime radical, cosocle | C22×C52 | C23 |
| hypocenter | C52 | C4×Q8 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #13099963, C8×#6039, #13100935, … |
| maximal normal subgroup of | #13099963, C8×#6039, #13100935, … |
| maximal quotient of | C8×#6039, #13100937, #13100941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 694);