Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1275 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic67 |
| commutator | C4×C67 | C4×C8 |
| Frattini | C2×C42 | C2×D67 |
| Fitting | C2×#97×C67 | C2 |
| socle | C22×C67 | #95 |
| hypercenter | C2×#97 | D67 |
| hypocenter | C67 | #1275 |
| LCS | G ▷ C4×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 | |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,e^a=ef,h^a=h^66,d^b=df1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742591, #30742592, #30742594, … |
| maximal normal subgroup of | #30742591, #30742592, #30742594, … |
| maximal quotient of | C67⋊#7014, #30742367, #30742369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2341);