Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#1132 |
| Fitting | C23×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #13260599, #13260603, #13260626, … |
| maximal normal subgroup of | #13260599, #13260603, #13260626, … |
| maximal quotient of | C23×#6395, C23×#6390, C23×#6391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18983);