Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#6467 |
| Fitting | C23×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C22×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | D28 |
| commutator, cosocle | C4×C7 | C25 |
| Frattini | C4 | C24×D7 |
| Fitting | C23×C7×C8 | C2 |
| socle | C23×C7 | C2×D4 |
| hypercenter | C23×C8 | D7 |
| hypocenter | C7 | C22×#135 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 | |
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #13260611, #13260613, #13260615, … |
| maximal normal subgroup of | #13260611, #13260613, #13260615, … |
| maximal quotient of | C22×#89885, C22×#89878, C22×C4×D56, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18984);