Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #41×Dic146 |
| Sylow | C73 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D73 |
| commutator, socle | C22×C73 | C25 |
| Frattini | C22 | C24×D73 |
| Fitting | C4×#41×C73 | C2 |
| hypercenter | C4×#41 | D73 |
| hypocenter | C73 | Q8×#41 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1068 conjugacy classes of subgroups.
1490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32978026, #32978030, #33052859, … |
| maximal normal subgroup of | #32978026, #32978030, #33052859, … |
| maximal quotient of | #41×#11924007, #41×C4⋊Dic73, #117×Dic146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 18090);