Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | D268 |
| commutator | C4×C67 | C2×C16 |
| Frattini | C2×C16 | C2×D67 |
| Fitting | C2×C32×C67 | C2 |
| socle | C2×C67 | C22⋊C16 |
| hypercenter | C2×C32 | D67 |
| hypocenter | C67 | #1401 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ C2×C32 | |
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,c^b=cg,d^b=dg,h^b=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1401×D67, C2×#22558350, #30776040, … |
| maximal normal subgroup of | #1401×D67, C2×#22558350, #30776040, … |
| maximal quotient of | #30743171, #30743231, #30743270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2651);