Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D67 |
| commutator, socle | C22×C67 | C2×C42 |
| Fitting | C82×C67 | C2 |
| hypercenter | C82 | D67 |
| hypocenter | C67 | #1454 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C42 ◁ C82 | |
178 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^c=h^662168 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1454×D67, C2×#22558508, #30821463, … |
| maximal normal subgroup of | #1454×D67, C2×#22558508, #30821463, … |
| maximal quotient of | #30745203, #30745221, #30746265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2809);