Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #554 |
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 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) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^18205 conjugacy classes — view the full character table.
| maximal subgroup of | #14575455, #14575457, #14575507, … |
| maximal normal subgroup of | #14575455, #14575457, #14575507, … |
| maximal quotient of | #14566508, #14566512, C4⋊C4×C22⋊D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1254);