Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #2335 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C7×#386 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C22×C7×D4 | C22 |
| hypercenter | #386 | D7 |
| hypocenter | C7 | #2335 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #386 | |
532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,d^2=ef,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×#2335, C2×#11732115, #13512726, … |
| maximal normal subgroup of | D7×#2335, C2×#11732115, #13512726, … |
| maximal quotient of | #13275060, #13275117, #13275132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 6881);