Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2480 |
664 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|b^2=ef,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^88,c^b=cg1798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2480×D89, C2×#26024498, #36722205, … |
| maximal normal subgroup of | #2480×D89, C2×#26024498, #36722205, … |
| maximal quotient of | #36476340, #36476638, #36477238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 8756);