Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#17989708 |
| Sylow | C73 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#10596842 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C2×D4×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C2×D4 | #10596842 |
| hypocenter | C73 | C2×#504 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
368 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
170 conjugacy classes — view the full character table.
| maximal subgroup of | #34034110, #34034111, #34034113, … |
| maximal normal subgroup of | #34034110, #34034111, #34034113, … |
| maximal quotient of | C2×#22627092, C2×#22627093, C4×#17989708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21760);