Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#532 ⋊ C2 |
| Sylow | C7 ⋊ #3480 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Frattini | C22 | C24×D7 |
| Fitting | C7×#532 | C2 |
| hypercenter | #532 | D7 |
| hypocenter | C7 | #3480 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,h^a=h^6,d^b=df,h^b=h^6134 conjugacy classes — view the full character table.
| maximal subgroup of | #13245822, #13245826, #13320681, … |
| maximal normal subgroup of | #13245822, #13245826, #13320681, … |
| maximal quotient of | #13513184, #13513188, #13513218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18054);