Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C67 ⋊ #2110 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C4×Dic67 |
| commutator | C4×C67 | C2×C42 |
| Frattini | C2×C8 | C22×D67 |
| Fitting | #405×C67 | C2 |
| socle | C2×C67 | C2×#97 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #2110 |
| LCS | G ▷ C4×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ #405 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,h^a=h^66,c^b=cg,d^b=dg1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30767013, #30767014, #30767017, … |
| maximal normal subgroup of | #30767013, #30767014, #30767017, … |
| maximal quotient of | #30764836, #30764840, #30764873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6115);