Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C22⋊C4×Dic73 |
| Sylow | C73 ⋊ C2×C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D73 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C23 | C23×D73 |
| Fitting | C22×C22⋊C4×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C22×C22⋊C4 | D73 |
| hypocenter | C73 | C2×C4×C22⋊C4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
1360 conjugacy classes of subgroups.
1520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #323×Dic73, #32976496, #32978639, … |
| maximal normal subgroup of | #323×Dic73, #32976496, #32978639, … |
| maximal quotient of | C2×#95×Dic73, C4×C22⋊C4×Dic73, C2×#22608153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6842);