Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1713 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #6437 |
| commutator, cosocle | C42×C7 | C23 |
| Frattini | C42 | C22×D7 |
| Fitting | C7×C82 | C2 |
| socle, prime radical | C22×C7 | #127 |
| hypercenter | C82 | D7 |
| hypocenter | C7 | #1713 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C82 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=f,b^2=df,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^6230 conjugacy classes — view the full character table.
| maximal subgroup of | #13240528, #13240530, #13240531, … |
| maximal normal subgroup of | #13240528, #13240530, #13240531, … |
| maximal quotient of | #13247577, #13253555, #13253563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 585);