Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C82×D7 |
| Fitting | C7×C82 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | D7 |
| commutator, hypocenter | C7 | C2×C82 |
| Frattini | C42 | C22×D7 |
| Fitting | C7×C82 | C2 |
| socle | C22×C7 | C2×C42 |
| prime radical | C22×D7 | C42 |
| cosocle | C42×C7 | C23 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C82 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D7×C16, D7×#1311, C8×#6372, … |
| maximal normal subgroup of | C8×D7×C16, D7×#1311, C8×#6372, … |
| maximal quotient of | C82×Dic7, D7×#1273, #13244218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 565);