Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D7×#459 |
| Fitting | C7×#459 ⋊ C2 |
| Sylow | C7 ⋊ C2×#459 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D7 |
| commutator, cosocle | C2×C4×C7 | C24 |
| Frattini | C2×C4 | C23×D7 |
| Fitting | C7×#459 | C2 |
| socle | C22×C7 | C22×D4 |
| hypercenter | #459 | D7 |
| hypocenter | C7 | C2×#459 |
| LCS | G ▷ C2×C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1619, D7×#1622, D7×#1625, … |
| maximal normal subgroup of | D7×#1619, D7×#1622, D7×#1625, … |
| maximal quotient of | D7×#1665, D7×#1667, D7×#1669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12541);