Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×#1142 |
| Sylow | C7 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13248355, #13248357, #13248375, … |
| maximal normal subgroup of | #13248355, #13248357, #13248375, … |
| maximal quotient of | C2×C8×#1142, C2×#11728618, C2×#11728596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14523);