Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2345 |
548 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 221 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=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | #13250228, #13250232, #13250256, … |
| maximal normal subgroup of | #13250228, #13250232, #13250256, … |
| maximal quotient of | C22⋊C4×C4⋊Dic7, #13275225, #13275284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5668);