Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C7 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D7 |
| commutator, socle | C2×C7 | C24×C4 |
| Fitting, prime radical | C7×#585 | C2 |
| cosocle | C4×C7 | C25 |
| hypercenter | #585 | D7 |
| hypocenter | C7 | #3573 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,f^2=g,h^a=h^6,e^b=eg,d^c=dg170 conjugacy classes — view the full character table.
| maximal subgroup of | #13359753, #13359759, #13359764, … |
| maximal normal subgroup of | #13359753, #13359759, #13359764, … |
| maximal quotient of | #14217217, #14217252, #14217433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19130);