Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #1740 |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=f,c^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | #13259008, #13259009, #13259257, … |
| maximal normal subgroup of | #13259008, #13259009, #13259257, … |
| maximal quotient of | #13243386, #13243392, #13243398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4113);