Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2324 |
668 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=ce,h^c=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36560149, #36560153, #36560179, … |
| maximal normal subgroup of | #36560149, #36560153, #36560179, … |
| maximal quotient of | #36475676, #36475721, #36475732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7204);