Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C67 ⋊ C2 |
| Sylow | C67 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C23×D67 |
| commutator, socle | C2×C67 | C24×C4 |
| Frattini | C4 | C24×D67 |
| Fitting | C2×#131×C67 | C2 |
| hypercenter | C2×#131 | D67 |
| hypocenter | C67 | #3573 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C2×#131 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=f,f^2=g,e^b=eg,d^c=dg,h^e=h^661388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30771278, #30771280, #30771281, … |
| maximal normal subgroup of | #30771278, #30771280, #30771281, … |
| maximal quotient of | #31719249, #31719250, #31719251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19221);