Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#17989667 |
| Sylow | C73 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C22×Q8×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C22×Q8 | #64408 |
| hypocenter | C73 | C2×#568 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
428 conjugacy classes — view the full character table.
| maximal subgroup of | #34008414, #34008424, #34008444, … |
| maximal normal subgroup of | #34008414, #34008424, #34008444, … |
| maximal quotient of | C2×#22626497, C2×#22626503, C4×#17989667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21504);