Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#41×Dic73 |
| Sylow | C73 ⋊ C2×C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C22 | C24×D73 |
| Fitting | C22×#41×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C22×#41 | D73 |
| hypocenter | C73 | C2×C4×#41 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
1728 conjugacy classes of subgroups.
1520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32991391, #32991394, #32991446, … |
| maximal normal subgroup of | #32991391, #32991394, #32991446, … |
| maximal quotient of | C2×#117×Dic73, C2×C4×D4×Dic73, C2×C4×Q8×Dic73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17692);