Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16838749 |
| Sylow | C241 ⋊ C2×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D241 |
| commutator | C2×C241 | C22×C4 |
| Frattini | C22 | C22×D241 |
| Fitting | C22×C4×C241 | C2 |
| socle | C23×C241 | C22 |
| hypercenter | C22×C4 | D241 |
| hypocenter | C241 | C2×C4⋊C4 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
92 conjugacy classes of subgroups.
1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507442, #29507568, C4×#16838749, … |
| maximal normal subgroup of | #29507442, #29507568, C4×#16838749, … |
| maximal quotient of | C2×#21440549, C4×#16838749, #29507575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 100);