Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D7×#548 |
| Fitting | C7×#548 ⋊ C2 |
| Sylow | C7 ⋊ C2×#548 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×#548 | C2 |
| hypercenter | #548 | D7 |
| hypocenter | C7 | C2×#548 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #548 | |
1620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3265, D7×#3269, D7×#3270, … |
| maximal normal subgroup of | D7×#3265, D7×#3269, D7×#3270, … |
| maximal quotient of | Q8×D7×C22⋊C4, D7×#2341, D7×#2351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18568);