Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C24×Dic146 |
| Sylow | C73 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D73 |
| commutator | C2×C73 | C26 |
| Frattini | C2 | C25×D73 |
| Fitting | C24×C4×C73 | C2 |
| socle | C25×C73 | C22 |
| hypercenter | C24×C4 | D73 |
| hypocenter | C73 | C24×Q8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
6264 conjugacy classes of subgroups.
2384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22608201, #33008369, #33008370, … |
| maximal normal subgroup of | C2×#22608201, #33008369, #33008370, … |
| maximal quotient of | C24×#11924007, C24×C4⋊Dic73, C23×C4×Dic146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19305);