Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#6399 |
| Fitting | C4×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13244503, C8×#6399, #13244510, … |
| maximal normal subgroup of | #13244503, C8×#6399, #13244510, … |
| maximal quotient of | C4×#89278, C4×#89279, #13244411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 2385);