Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #407×C67 ⋊ C2 |
| Sylow | C67 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | #407×C67 | C2 |
| hypercenter | #407 | D67 |
| hypocenter | C67 | D4×M16 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
544 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,d^c=dg,h^c=h^66974 conjugacy classes — view the full character table.
| maximal subgroup of | #30871176, #30871178, #30871184, … |
| maximal normal subgroup of | #30871176, #30871178, #30871184, … |
| maximal quotient of | #30827249, #30827257, #30827265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13242);