Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D241 |
| Fitting | M16×C241 ⋊ C2 |
| Sylow | C241 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D241 |
| commutator, socle | C2×C241 | C22×C4 |
| Fitting | M16×C241 | C2 |
| hypercenter | M16 | D241 |
| hypocenter | C241 | C2×M16 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C4 ◁ M16 | |
68 conjugacy classes of subgroups.
1220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D241, #101×D241, #29507698, … |
| maximal normal subgroup of | #100×D241, #101×D241, #29507698, … |
| maximal quotient of | #97×D241, M16×Dic241, #29507669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 149);