Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D67 |
| commutator, socle | C22×C67 | C22×C8 |
| Fitting | C2×C4×C8×C67 | C2 |
| hypercenter | C2×C4×C8 | D67 |
| hypocenter | C67 | #2150 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C4×C8 | |
172 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742695, #30742696, #30742698, … |
| maximal normal subgroup of | #30742695, #30742696, #30742698, … |
| maximal quotient of | #30767376, #30767402, #30767435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6266);