Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #518×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator | C2×C67 | C24×C4 |
| Fitting | #518×C67 | C2 |
| socle | C22×C67 | C25 |
| hypercenter | #518 | D67 |
| hypocenter | C67 | #3428 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #518 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^e=h^661190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30855687, #30855699, #30856643, … |
| maximal normal subgroup of | #30855687, #30855699, #30856643, … |
| maximal quotient of | #31014042, #31014044, #31014056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17708);