Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C19×H(5,𝔽2) ⋊ C2 |
| Sylow | C19 ⋊ #576 |
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^18,d^c=df175 conjugacy classes — view the full character table.
| maximal subgroup of | #14575396, #14575397, #14575399, … |
| maximal normal subgroup of | #14575396, #14575397, #14575399, … |
| maximal quotient of | #14572158, #14572161, #14572233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1352);