Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
606 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^4,3,2^4|a^2=d,c^2=d,c^a=cd,e^a=e^2,f^a=fg,h^a=hi,f^b=fh,g^b=gi,f^e=g,g^e=fg,h^e=i,i^e=hi38 conjugacy classes — view the full character table.
| maximal subgroup of | Q8×#1020⋊C2, #72241511, #72241513, … |
| maximal normal subgroup of | Q8×#1020⋊C2, #72241511, #72241513, … |
| maximal quotient of | #72341564, #72341577 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087698);