Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×D4×C5⋊D5 |
| Fitting | C2×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C5⋊D5 |
| commutator, cosocle | C2×C52 | C24 |
| Frattini | C2 | C23×C5⋊D5 |
| Fitting | C2×C52×D4 | C2 |
| socle | C22×C52 | C23 |
| hypercenter | C2×D4 | C5⋊D5 |
| hypocenter | C52 | C22×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
944 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13101582, #13101587, #13101596, … |
| maximal normal subgroup of | #13101582, #13101587, #13101596, … |
| maximal quotient of | C2×#11717198, C2×#11717205, C2×C22⋊C4×C5⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1174);