Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C7×#124 ⋊ C2 |
| Sylow | C7 ⋊ #3561 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C2×C7×#124 | C2 |
| hypercenter | C2×#124 | D7 |
| hypocenter | C7 | #3561 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×#124 | |
1032 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=f,d^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^6,c^b=cg,d^b=df,h^b=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | #13246100, #13246104, #13246261, … |
| maximal normal subgroup of | #13246100, #13246104, #13246261, … |
| maximal quotient of | #13516739, #13516807, #13517054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17915);