Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #1442 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D7 |
| commutator | C23×C7 | C22×C4 |
| Fitting | C2×C7×#95 | C2 |
| socle, prime radical, cosocle | C24×C7 | C23 |
| hypercenter | C2×#95 | D7 |
| hypocenter | C7 | #1442 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=e,c^2=d,b^a=bd,c^a=ce,c^b=cf,h^b=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1442, C2×#11727167, #13275490, … |
| maximal normal subgroup of | D7×#1442, C2×#11727167, #13275490, … |
| maximal quotient of | #13241719, #13241720, #13241722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 1933);