Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C67 ⋊ #1729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D67 |
| commutator | C22×C67 | C2×C42 |
| Fitting | C23×C8×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C23×C8 | D67 |
| hypocenter | C67 | #1729 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C8 | |
416 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=f,e^2=g,b^a=bd,c^b=cg,h^b=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742785, #30742787, #30761183, … |
| maximal normal subgroup of | #30742785, #30742787, #30761183, … |
| maximal quotient of | #30745213, #30745216, #30745219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4206);