Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D7×#520 |
| Fitting | C7×#520 ⋊ C2 |
| Sylow | C7 ⋊ C2×#520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator | C2×C7 | C24×C4 |
| Fitting | C7×#520 | C2 |
| socle, cosocle | C22×C7 | C25 |
| prime radical | C2×D7×#41 | C2 |
| hypercenter | #520 | D7 |
| hypocenter | C7 | C2×#520 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1859, D7×#1860, #13354671, … |
| maximal normal subgroup of | D7×#1859, D7×#1860, #13354671, … |
| maximal quotient of | D7×#2274, D7×#2275, D7×#2276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17733);