Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #1664 |
184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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=f,b^2=g,c^2=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,h^b=h^88,d^c=dg,e^c=efg,h^c=h^88724 conjugacy classes — view the full character table.
| maximal subgroup of | #1664×D89, C2×#26019585, #36535602, … |
| maximal normal subgroup of | #1664×D89, C2×#26019585, #36535602, … |
| maximal quotient of | #36443297, #36443303, #36443310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3843);