Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #41×#10596842 |
| Fitting | #41×C73 ⋊ C8 |
| Sylow | C73 ⋊ C8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#10596842 |
| commutator, socle | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | #41×C73 | C8 |
| hypercenter | #41 | #10596842 |
| hypocenter | C73 | C8×#41 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ #41 | |
456 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 197 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 | #104×#10596842, #34033276, #34033390, … |
| maximal normal subgroup of | #104×#10596842, #34033276, #34033390, … |
| maximal quotient of | #117×#10596842, C4×D4×#10596842, C4×Q8×#10596842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21751);