Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#6553 |
| Fitting | C4×C7×#41 ⋊ C2 |
| Sylow | C7 ⋊ C4×H(5,𝔽2) |
1660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #13245193, #13245196, #13320174, … |
| maximal normal subgroup of | #13245193, #13245196, #13320174, … |
| maximal quotient of | C4×#90236, C4×#90212, C4×#90214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17669);