Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C67 ⋊ #1446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D67 |
| commutator | C23×C67 | C22×C4 |
| Fitting | C23×Q8×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C23×Q8 | D67 |
| hypocenter | C67 | #1446 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
736 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=f,c^2=f,b^a=bd,c^a=ce,h^a=h^66,c^b=cf1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30743111, #30747968, #30747969, … |
| maximal normal subgroup of | #30743111, #30747968, #30747969, … |
| maximal quotient of | #30743758, #30764738, #30764741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2781);