Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16838757 |
| Fitting | C2×Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D241 |
| commutator | C4×C241 | C23 |
| Frattini | C4 | C22×D241 |
| Fitting | C2×Q8×C241 | C2 |
| socle | C22×C241 | D4 |
| hypercenter | C2×Q8 | D241 |
| hypocenter | C241 | C2×SD16 |
| LCS | G ▷ C4×C241 ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
1214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507802, C4×#16838757, #29507815, … |
| maximal normal subgroup of | #29507802, C4×#16838757, #29507815, … |
| maximal quotient of | C2×#21440562, C2×#21440566, C2×#21440573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 159);