Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C22⋊D67 |
| commutator | C4×C67 | C2×C16 |
| Frattini | C2×C16 | C2×D67 |
| Fitting | #504×C67 | C2 |
| socle | C2×C67 | C22⋊C16 |
| hypercenter | #504 | D67 |
| hypocenter | C67 | #1401 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ #504 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^66,c^b=cg,d^b=dg1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1401×D67, C2×#22558351, #30776040, … |
| maximal normal subgroup of | #1401×D67, C2×#22558351, #30776040, … |
| maximal quotient of | #30743172, #30743232, D4⋊(C67⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2652);