Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #332×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1550 |
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=e,b^2=g,c^2=f,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^88,h^c=h^88868 conjugacy classes — view the full character table.
| maximal subgroup of | #1550×D89, C2×#26018941, #36522783, … |
| maximal normal subgroup of | #1550×D89, C2×#26018941, #36522783, … |
| maximal quotient of | #36442434, #36442492, #36442598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3199);