Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D4×C22⋊D7 |
| Fitting | C23×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D7 |
| commutator, cosocle | C22×C7 | C25 |
| Frattini | C22 | C24×D7 |
| Fitting | C23×C7×D4 | C2 |
| socle | C23×C7 | C24 |
| hypercenter | C23×D4 | D7 |
| hypocenter | C7 | C2×D42 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
2536 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13245458, #13369114, D4×#6380, … |
| maximal normal subgroup of | #13245458, #13369114, D4×#6380, … |
| maximal quotient of | C2×D4×(C2×D7)⋊C4, C2×C22⋊C4×C22⋊D7, C2×D4×C22⋊Dic7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19072);