Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C67 ⋊ #3501 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | #518×C67 | C2 |
| hypercenter | #518 | D67 |
| hypocenter | C67 | #3501 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #518 | |
1100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,c^2=g,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^661166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30892053, #30892055, #30892071, … |
| maximal normal subgroup of | #30892053, #30892055, #30892071, … |
| maximal quotient of | #31015917, #31016252, #31016264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 18308);