Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C181 ⋊ C2 |
| Sylow | C181 ⋊ #399 |
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,181|a^2=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^c=g^1801822 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37532739, #37532744, #37532766, … |
| maximal normal subgroup of | #37532739, #37532744, #37532766, … |
| maximal quotient of | #37531963, #37531965, #37531984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 484);