Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D7 |
| commutator, socle | C2×C7 | C22×C16 |
| Fitting | C7×#504 | C2 |
| prime radical | C7×#41 | C8 |
| cosocle | C7×C16 | C23 |
| hypercenter | #504 | D7 |
| hypocenter | C7 | #2258 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C16 ◁ #504 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^6,c^b=cg200 conjugacy classes — view the full character table.
| maximal subgroup of | #13274357, #13274360, #13274362, … |
| maximal normal subgroup of | #13274357, #13274360, #13274362, … |
| maximal quotient of | #13273976, #13273993, #13274282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3971);