Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×D292 |
| Fitting | C4×C22⋊C4×C73 ⋊ C2 |
| Sylow | C73 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator | C22×C73 | C23×C4 |
| Fitting | C4×C22⋊C4×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C4×C22⋊C4 | D73 |
| hypocenter | C73 | D4×C22⋊C4 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
1252 conjugacy classes of subgroups.
1490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32982402, #32982406, #32982430, … |
| maximal normal subgroup of | #32982402, #32982406, #32982430, … |
| maximal quotient of | C22⋊C4×#11924005, C22⋊C4×C4⋊Dic73, #95×D292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7333);