Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16838771 |
| Fitting | C2×Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D241 |
| commutator | C2×C241 | C24 |
| Frattini | C2 | C23×D241 |
| Fitting | C2×Q8×C241 | C2 |
| socle | C22×C241 | C23 |
| hypercenter | C2×Q8 | D241 |
| hypocenter | C241 | C2×#41 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
1220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507700, #29507712, #29507717, … |
| maximal normal subgroup of | #29507700, #29507712, #29507717, … |
| maximal quotient of | C2×#21440600, C2×#21440604, C2×Q8×Dic241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 190);