Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87721 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#87722 |
| Fitting | C2×D4×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×D8 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #13098024, #13098032, #13098037, … |
| maximal normal subgroup of | #13098024, #13098032, #13098037, … |
| maximal quotient of | C2×#11716355, C2×#11716358, #13098245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 153);