Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#16863877 |
| Fitting | C22×C4⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#520 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D67 |
| commutator | C2×C67 | C24×C4 |
| Frattini | C22 | C24×D67 |
| Fitting | C22×C4⋊C4×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C22×C4⋊C4 | D67 |
| hypocenter | C67 | C2×#520 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
1640 conjugacy classes of subgroups.
1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30761267, #30761311, #30761347, … |
| maximal normal subgroup of | #30761267, #30761311, #30761347, … |
| maximal quotient of | C2×#22562563, C2×#22562566, C2×#22562567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17705);