Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87771 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#87771 |
| Sylow | C52 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #6038 |
| commutator, cosocle | C4×C52 | C23 |
| Frattini | C4 | C2×D52 |
| Fitting | C2×C4×C52 | C22 |
| socle | C22×C52 | D4 |
| hypercenter | C2×C4 | D52 |
| hypocenter | C52 | C2×D8 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
206 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#87771, #13100524, #13100527, … |
| maximal normal subgroup of | C4×#87771, #13100524, #13100527, … |
| maximal quotient of | #13100450, #13100451, #13100459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 601);