Finite Group DatabasebetaFinite Group Databasebeta| order | 10592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×D4×C331 ⋊ C2 |
| Sylow | C331 ⋊ #127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D331 |
| commutator, socle, cosocle | C22×C331 | C23 |
| Fitting | C2×D4×C331 | C2 |
| hypercenter | C2×D4 | D331 |
| hypocenter | C331 | #127 |
| LCS | G ▷ C22×C331 ▷ C331 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,331|b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^3301664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35233184, #35233558, #35233560, … |
| maximal normal subgroup of | #35233184, #35233558, #35233560, … |
| maximal quotient of | #35233261, #35233292, #35233293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10592, 142);