Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #444×D67 |
| Fitting | #444×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D67 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #444×C67 | C2 |
| socle | C2×C67 | C2×C4×D4 |
| hypercenter | #444 | D67 |
| hypocenter | C67 | C2×#444 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #444 | |
464 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #2180×D67, AGL(1,ℤ/16)×D67, #31009276, … |
| maximal normal subgroup of | #2180×D67, AGL(1,ℤ/16)×D67, #31009276, … |
| maximal quotient of | SD16⋊C8×D67, #1579×D67, #1580×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13402);