Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#10596842 |
| Fitting | M16×C73 ⋊ C8 |
| Sylow | C73 ⋊ C8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#10596842 |
| commutator, socle | C2×C73 | C2×C4×C8 |
| Fitting | M16×C73 | C8 |
| hypercenter | M16 | #10596842 |
| hypocenter | C73 | C8×M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ M16 | |
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21618);