Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#17988460 |
| Sylow | C73 ⋊ C2×#385 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C23 | C23×D73 |
| Fitting | C24×C4×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C24×C4 | D73 |
| hypocenter | C73 | C2×#385 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
1232 conjugacy classes of subgroups.
2360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32981363, #32981365, #32981383, … |
| maximal normal subgroup of | #32981363, #32981365, #32981383, … |
| maximal quotient of | C2×#22608154, C2×#22608164, C4×#17988460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6921);