Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×D7×D8 |
| Fitting | C22×C7×D8 ⋊ C2 |
| Sylow | C7 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D7 |
| commutator, cosocle | C4×C7 | C25 |
| Frattini | C4 | C24×D7 |
| Fitting | C22×C7×D8 | C2 |
| socle | C23×C7 | C2×D4 |
| hypercenter | C22×D8 | D7 |
| hypocenter | C7 | C23×D8 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1976 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) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13269436, #13269457, D7×#1879, … |
| maximal normal subgroup of | #13269436, #13269457, D7×#1879, … |
| maximal quotient of | C22×D7×#102, C22×D7×#107, C2×C4×D7×D8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19003);