Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
1313 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 1313 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^4,3,2^4|a^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=fg,h^a=hi,f^e=g,g^e=fg,h^e=i,i^e=hi56 conjugacy classes — view the full character table.
| maximal subgroup of | #72227806, C2×#11715649, #72228080, … |
| maximal normal subgroup of | C2×#11715649, M16×#1020, #72234216, … |
| maximal quotient of | C2×#11715649, #72269845, #72342009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1090030);