Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C67 ⋊ C2 |
| Sylow | C67 ⋊ #1335 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D536 |
| commutator | C8×C67 | C2×C8 |
| Frattini | C4×C8 | C2×D67 |
| Fitting | C82×C67 | C2 |
| socle | C2×C67 | D4⋊C8 |
| hypercenter | C82 | D67 |
| hypocenter | C67 | #1335 |
| LCS | G ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^66,c^b=ce,e^b=eg,h^b=h^662156 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1335×D67, C2×#22558183, #30765616, … |
| maximal normal subgroup of | #1335×D67, C2×#22558183, #30765616, … |
| maximal quotient of | #30742481, #30742484, #30742499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2484);