Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D7×#472 |
| Fitting | C7×#472 ⋊ C2 |
| Sylow | C7 ⋊ C2×#472 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D7×#121 |
| commutator, cosocle | C2×C4×C7 | C24 |
| Frattini | C2×C4 | C23×D7 |
| Fitting | C7×#472 | C2 |
| socle | C2×C7 | C2×#121 |
| hypercenter | #472 | D7 |
| hypocenter | C7 | C2×#472 |
| LCS | G ▷ C2×C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2192, D7×#2193, #13507776, … |
| maximal normal subgroup of | D7×#2192, D7×#2193, #13507776, … |
| maximal quotient of | D7×#1667, D7×#1675, D7×#1677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 13147);