Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C7×#388 ⋊ C2 |
| Sylow | C7 ⋊ #2576 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#388 | C2 |
| prime radical | C22×C22⋊D7 | C22 |
| hypercenter | #388 | D7 |
| hypocenter | C7 | #2576 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #388 | |
468 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=ef,d^2=f,b^a=beg,c^a=cf,d^a=deg,h^a=h^6,c^b=cg,h^b=h^6,h^c=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2576, C2×#11733337, #13524293, … |
| maximal normal subgroup of | D7×#2576, C2×#11733337, #13524293, … |
| maximal quotient of | #13276144, #13276405, #13276765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 8103);