Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C89 ⋊ #3504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | C4×#41×C89 | C2 |
| prime radical | C2×#41×C89 | C22 |
| hypercenter | C4×#41 | D89 |
| hypocenter | C89 | #3504 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 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,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^88,d^b=df1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36446693, #36522675, #36522702, … |
| maximal normal subgroup of | #36446693, #36522675, #36522702, … |
| maximal quotient of | #36714539, #36714888, #36714908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 18336);