Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×C7⋊C8 |
| derived, Sylow | C7 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D7 |
| commutator, hypocenter | C7 | C24×C8 |
| Frattini | C4 | C24×D7 |
| Fitting | C24×C4×C7 | C2 |
| socle, prime radical | C25×C7 | C4 |
| cosocle | C4×C7 | C25 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13259019, #13259021, #13259045, … |
| maximal normal subgroup of | #13259019, #13259021, #13259045, … |
| maximal quotient of | C23×C4×C7⋊C8, C23×C22⋊(C7⋊C8), C23×C4⋊(C7⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19046);