Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#11924037 |
| Sylow | C73 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | C22×D4×C73 | C4 |
| hypercenter | C22×D4 | #64408 |
| hypocenter | C73 | D4×M16 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
544 conjugacy classes of subgroups.
410 conjugacy classes — view the full character table.
| maximal subgroup of | #34006632, #34006636, #34006640, … |
| maximal normal subgroup of | #34006632, #34006636, #34006640, … |
| maximal quotient of | D8×#11924037, #34019386, SD16×#11924037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21246);