Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4×C5 |
| direct product | C4×#6034 |
| derived, Sylow | C52 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1044 |
| commutator, hypocenter | C52 | C4×C8 |
| Frattini | C22 | C2×#1044 |
| Fitting | C2×C4×C52 | C4 |
| socle, prime radical | C22×C52 | C2×C4 |
| cosocle | C2×#1039 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13099874, #13099875, #13099876, … |
| maximal normal subgroup of | #13099874, #13099875, #13099876, … |
| maximal quotient of | C4×#87765, #13100328, C8×#6034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 552);