Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D100 |
| Fitting | C22×C4×C25 ⋊ C2 |
| Sylow | C25 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D25 |
| commutator, cosocle | C2×C25 | C24 |
| Frattini | C2×C5 | C23×D5 |
| Fitting | C22×C4×C25 | C2 |
| socle | C23×C5 | C2×D5 |
| hypercenter | C22×C4 | D25 |
| hypocenter | C25 | C22×D4 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097944, #13097948, #13097949, … |
| maximal normal subgroup of | #13097944, #13097948, #13097949, … |
| maximal quotient of | C2×#11716431, C2×C4×D100, C2×#11716436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 218);