Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #520 |
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^18214 conjugacy classes — view the full character table.
| maximal subgroup of | #14563860, #14563864, #14563867, … |
| maximal normal subgroup of | #14563860, #14563864, #14563867, … |
| maximal quotient of | #14565989, #14565992, #14565993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1030);