Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C67 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D67 |
| commutator, socle | C2×C67 | C23×C8 |
| Fitting | C2×#131×C67 | C2 |
| hypercenter | C2×#131 | D67 |
| hypocenter | C67 | #3407 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C2×#131 | |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,e^2=f,f^2=g,d^a=dg,h^a=h^66,c^b=cg1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30770959, #30770961, #30771990, … |
| maximal normal subgroup of | #30770959, #30770961, #30771990, … |
| maximal quotient of | #31008472, #31008481, #31008509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17613);