Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2337 |
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=ce1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36451714, #36451718, #36451728, … |
| maximal normal subgroup of | #36451714, #36451718, #36451728, … |
| maximal quotient of | #36475704, #36475763, #36475768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7323);