Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C24×Dic134 |
| Sylow | C67 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D67 |
| commutator | C2×C67 | C26 |
| Frattini | C2 | C25×D67 |
| Fitting | C24×C4×C67 | C2 |
| socle | C25×C67 | C22 |
| hypercenter | C24×C4 | D67 |
| hypocenter | C67 | C24×Q8 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
6264 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22558479, #30778216, #30778217, … |
| maximal normal subgroup of | C2×#22558479, #30778216, #30778217, … |
| maximal quotient of | C24×Dic67⋊C4, C24×C4⋊Dic67, C23×C4×Dic134, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19305);