Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#14556638 |
| Fitting | C4×#41×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D73 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C22 | C24×D73 |
| Fitting | C4×#41×C73 | C2 |
| socle | C22×C73 | C25 |
| hypercenter | C4×#41 | D73 |
| hypocenter | C73 | C4×2−1+4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1492 conjugacy classes of subgroups.
1508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32977386, #32977389, #33052369, … |
| maximal normal subgroup of | #32977386, #32977389, #33052369, … |
| maximal quotient of | C4×#17989067, C4×#17989066, C4×#17989070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17720);