Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #398×D67 |
| Fitting | #398×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | #398×C67 | C2 |
| hypercenter | #398 | D67 |
| hypocenter | C67 | C2×#398 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ #398 | |
692 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | #1346×D67, #30766515, #1609×D67, … |
| maximal normal subgroup of | #1346×D67, #30766515, #1609×D67, … |
| maximal quotient of | #1441×D67, #1442×D67, #1444×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7739);