Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×D73⋊#131 |
| unambiguous semidirect product | D73⋊(C2×#131) |
| Sylow | C73 ⋊ C22×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C2×#41×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C2×#41 | #64408 |
| hypocenter | C73 | C22×#131 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
1504 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #34008471, #34008474, #34008515, … |
| maximal normal subgroup of | #34008471, #34008474, #34008515, … |
| maximal quotient of | C2×#22626491, C2×C4×#14556678, C4×D73⋊#131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21499);