Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #2367 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^6,d^b=de,h^b=h^6134 conjugacy classes — view the full character table.
| maximal subgroup of | #13376084, #13376086, #13376099, … |
| maximal normal subgroup of | #13376084, #13376086, #13376099, … |
| maximal quotient of | #13275244, #13275338, #13275365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15166);