Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3444 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D67 |
| commutator, socle | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C4×#41×C67 | C2 |
| hypercenter | C4×#41 | D67 |
| hypocenter | C67 | #3444 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C42 ◁ C4×#41 | |
1212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|d^2=g,e^2=f,b^a=bf,c^a=cg,h^c=h^661376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30771416, #30822340, #30822363, … |
| maximal normal subgroup of | #30771416, #30822340, #30822363, … |
| maximal quotient of | #31014130, #31014233, #31014237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17803);