Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C82×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1712 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #15668009 |
| commutator, cosocle | C42×C89 | C23 |
| Frattini | C42 | C22×D89 |
| Fitting | C82×C89 | C2 |
| socle | C22×C89 | #127 |
| hypercenter | C82 | D89 |
| hypocenter | C89 | #1712 |
| LCS | G ▷ C42×C89 ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C82 | |
280 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|b^2=df,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^882854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36441158, #36467823, #36468600, … |
| maximal normal subgroup of | #36441158, #36467823, #36468600, … |
| maximal quotient of | #36448209, #36454191, #36457197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4125);