Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C23×C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #386 |
286 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=df,b^a=bd,c^a=ce,g^a=g^18316 conjugacy classes — view the full character table.
| maximal subgroup of | #14563582, #14563914, #14564884, … |
| maximal normal subgroup of | #14563582, #14563914, #14564884, … |
| maximal quotient of | #14561858, #14561868, #14561873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 428);