Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #520×C67 ⋊ C2 |
| Sylow | C67 ⋊ C4×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator | C2×C67 | C24×C4 |
| Fitting | #520×C67 | C2 |
| socle | C22×C67 | C25 |
| hypercenter | #520 | D67 |
| hypocenter | C67 | C4×H(5,𝔽2) |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,h^d=h^66,h^e=h^661190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30861702, #30861708, #30861713, … |
| maximal normal subgroup of | #30861702, #30861708, #30861713, … |
| maximal quotient of | #31014063, #31014065, #31014069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17716);