Finite Group DatabasebetaFinite Group Databasebeta| order | 7664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D1916 |
| Fitting | C2×C4×C479 ⋊ C2 |
| Sylow | C479 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D479 |
| commutator | C2×C479 | C23 |
| Frattini | C2 | C22×D479 |
| Fitting | C2×C4×C479 | C2 |
| socle | C22×C479 | C22 |
| hypercenter | C2×C4 | D479 |
| hypocenter | C479 | C2×D4 |
| LCS | G ▷ C2×C479 ▷ C479 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
1922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29506298, #29506302, #29506304, … |
| maximal normal subgroup of | #29506298, #29506302, #29506304, … |
| maximal quotient of | C2×(C2×D479)⋊C4, C2×C4⋊Dic479, C4×D1916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7664, 36);