Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C67 ⋊ #1839 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D67 |
| commutator | C22×C67 | C22×C8 |
| Fitting | C43×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C43 | D67 |
| hypocenter | C67 | #1839 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742366, #30742367, #30742377, … |
| maximal normal subgroup of | #30742366, #30742367, #30742377, … |
| maximal quotient of | #30749551, #30749555, #30761436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4653);