Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D7×#435 |
| Fitting | C7×#435 ⋊ C2 |
| Sylow | C7 ⋊ C2×#435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D7 |
| commutator, socle | C22×C7 | C23×C4 |
| Fitting | C7×#435 | C2 |
| prime radical | C2×D4×D7 | C4 |
| cosocle | C2×C4×C7 | C24 |
| hypercenter | #435 | D7 |
| hypocenter | C7 | C2×#435 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #435 | |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D7×#435, D7×#2929, D7×#2930, … |
| maximal normal subgroup of | C2×D7×#435, D7×#2929, D7×#2930, … |
| maximal quotient of | D7×#1581, D7×#1583, D7×#1582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11688);