Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×C22⋊D7 |
| Fitting | C22×C7×#41 ⋊ C2 |
| Sylow | C7 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Frattini | C22 | C24×D7 |
| Fitting | C22×C7×#41 | C2 |
| hypercenter | C22×#41 | D7 |
| hypocenter | C7 | D4×#41 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13369463, #104×C22⋊D7, #13369474, … |
| maximal normal subgroup of | #13369463, #104×C22⋊D7, #13369474, … |
| maximal quotient of | #41×(C2×D7)⋊C4, #41×C22⋊Dic7, #41×Dic7⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19106);