Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C7×#131 ⋊ C2 |
| Sylow | C7 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C23×D7 |
| commutator, socle | C2×C7 | C24×C4 |
| Frattini | C4 | C24×D7 |
| Fitting | C2×C7×#131 | C2 |
| prime radical | #90616 | C2 |
| cosocle | C4×C7 | C25 |
| hypercenter | C2×#131 | D7 |
| hypocenter | C7 | #3573 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C8 ◁ C2×#131 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,f^2=g,e^b=eg,h^b=h^6,d^c=dg188 conjugacy classes — view the full character table.
| maximal subgroup of | #13269243, #13269245, #13269246, … |
| maximal normal subgroup of | #13269243, #13269245, #13269246, … |
| maximal quotient of | #14217214, #14217215, #14217216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18994);