Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #2295 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C22×C67 | C23×C4 |
| Frattini | C23 | C23×D67 |
| Fitting | C4×C4⋊C4×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C4×C4⋊C4 | D67 |
| hypocenter | C67 | #2295 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
500 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^b=h^66,h^c=h^661376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30854441, #30854442, #30854461, … |
| maximal normal subgroup of | #30854441, #30854442, #30854461, … |
| maximal quotient of | #30776941, #30776960, #30776961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6986);