Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#87764 |
| derived, Sylow | C52 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1043 |
| commutator, hypocenter | C52 | C2×C16 |
| Frattini | C4 | C2×#1043 |
| Fitting | C2×C4×C52 | C4 |
| socle, prime radical | C22×C52 | C8 |
| cosocle | #6029 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C4 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13099918, #13099919, #13099921, … |
| maximal normal subgroup of | #13099918, #13099919, #13099921, … |
| maximal quotient of | C4×#87764, C4⋊#87764, C2×#11716580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 524);