Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C4×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #2341 |
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=e,c^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | #13369528, #13369529, #13369547, … |
| maximal normal subgroup of | #13369528, #13369529, #13369547, … |
| maximal quotient of | #13275217, Q8×C7⋊#95, #13275364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14668);