Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#90448 |
| Fitting | C22×C7×D8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D7 |
| commutator, cosocle | C4×C7 | C25 |
| Frattini | C4 | C24×D7 |
| Fitting | C22×C7×D8 | C2 |
| socle | C22×C7 | C22×D4 |
| hypercenter | C22×D8 | D7 |
| hypocenter | C7 | C2×#576 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×D8 | |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13269480, #13269492, #13269519, … |
| maximal normal subgroup of | #13269480, #13269492, #13269519, … |
| maximal quotient of | C2×#11736187, C2×#11736591, C2×#11737032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19006);