Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic67 |
| commutator | C4×C67 | C4×C8 |
| Frattini | C4×C8 | C2×D67 |
| Fitting | #322×C67 | C2 |
| socle | C22×C67 | #97 |
| hypercenter | #322 | D67 |
| hypocenter | C67 | #1313 |
| LCS | G ▷ C4×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #322 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^66,c^b=cg1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1313×D67, C2×#22558130, #30764830, … |
| maximal normal subgroup of | #1313×D67, C2×#22558130, #30764830, … |
| maximal quotient of | #30742448, #30742661, #30743167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2431);