Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C67 ⋊ #1367 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | D268 |
| commutator | C4×C67 | C2×C16 |
| Frattini | C4×C8 | C2×D67 |
| Fitting | C82×C67 | C2 |
| socle | C22×C67 | C4⋊C8 |
| hypercenter | C82 | D67 |
| hypocenter | C67 | #1367 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=c,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742486, #30742487, #30742489, … |
| maximal normal subgroup of | #30742486, #30742487, #30742489, … |
| maximal quotient of | #30742569, #30742694, #30743497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2574);