Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4×C5 |
| direct product | C2×C4×#1044 |
| Fitting | C2×C4×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1044 |
| commutator, hypocenter | C52 | C2×C42 |
| Frattini | C2 | C22×#1044 |
| Fitting | C2×C4×C52 | C4 |
| socle | C22×C52 | C2×C4 |
| prime radical | C22×C5⋊D5 | C22 |
| cosocle | C2×C5⋊D5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13099894, #13099901, #13099902, … |
| maximal normal subgroup of | #13099894, #13099901, #13099902, … |
| maximal quotient of | C4×#87862, #13104814, C4×#87863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1108);