Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C43×D7 |
| Fitting | C43×C7 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D7 |
| commutator, hypocenter | C7 | C2×C43 |
| Frattini | C23 | C23×D7 |
| Fitting | C43×C7 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C23×D7 | C23 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C43 | |
1272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×#1276, #13243236, C42×C8×D7, … |
| maximal normal subgroup of | D7×#1276, #13243236, C42×C8×D7, … |
| maximal quotient of | C43×Dic7, C4×D7×#95, C4×#89420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5523);