Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#388 ⋊ C2 |
| Sylow | C7 ⋊ #2322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C7×#388 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C22×C22⋊D7 | C22 |
| hypercenter | #388 | D7 |
| hypocenter | C7 | #2322 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #388 | |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^6,c^b=ce,h^d=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2322, C2×#11733273, #13512555, … |
| maximal normal subgroup of | D7×#2322, C2×#11733273, #13512555, … |
| maximal quotient of | #13275038, #13275080, #13275094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 8039);