Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#120×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2021 |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^c=dg,h^c=h^881258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2021×D89, C2×#26021375, #36581668, … |
| maximal normal subgroup of | #2021×D89, C2×#26021375, #36581668, … |
| maximal quotient of | #36454621, #36454624, #36454628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5633);