Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ Q8×Q16 |
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=eg,c^2=g,d^2=eg,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^6,d^b=deg,h^b=h^6,f^c=fg,h^c=h^6101 conjugacy classes — view the full character table.
| maximal subgroup of | #13267483, #13267487, #13267511, … |
| maximal normal subgroup of | #13267483, #13267487, #13267511, … |
| maximal quotient of | #13370400, #13372226, #13372227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14167);