Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2651 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=eg,b^2=e,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^881792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2651×D89, C2×#26026279, #36721128, … |
| maximal normal subgroup of | #2651×D89, C2×#26026279, #36721128, … |
| maximal quotient of | #36480897, #36480986, #36481046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10537);