Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C67 ⋊ #1312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D67 |
| commutator | C2×C67 | C4×C16 |
| Fitting | C4×C16×C67 | C2 |
| socle | C22×C67 | C4×C8 |
| hypercenter | C4×C16 | D67 |
| hypocenter | C67 | #1312 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4×C8 ◁ C4×C16 | |
92 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^662192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1312×D67, C2×#22558128, #30764819, … |
| maximal normal subgroup of | #1312×D67, C2×#22558128, #30764819, … |
| maximal quotient of | #30742448, #30742658, #30743163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2429);