Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#396 ⋊ C2 |
| Sylow | C7 ⋊ #2820 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#396 | C2 |
| prime radical | C22×C22⋊D7 | C22 |
| hypercenter | #396 | D7 |
| hypocenter | C7 | #2820 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #396 | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=ef,d^2=ef,b^a=bef,c^a=cf,c^b=cg,d^b=de,d^c=def,h^d=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2820, C2×#11734847, #13560345, … |
| maximal normal subgroup of | D7×#2820, C2×#11734847, #13560345, … |
| maximal quotient of | #13284464, #13284467, #13284486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 9613);