Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #342 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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|a^2=d,b^2=e,b^a=bc,c^a=cf,d^b=df,g^b=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#342, C2×#11926310, #14563366, … |
| maximal normal subgroup of | D19×#342, C2×#11926310, #14563366, … |
| maximal quotient of | #14561477, #14561481, #14561483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 315);