Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | #334×D73 |
| Fitting | #334×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#334 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D73 |
| commutator | C4×C73 | C22×C8 |
| Frattini | C42 | C22×D73 |
| Fitting | #334×C73 | C2 |
| socle | C22×C73 | C2×C4⋊C4 |
| hypercenter | #334 | D73 |
| hypocenter | C73 | C2×#334 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #334 | |
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1333×D73, #1334×D73, #32995752, … |
| maximal normal subgroup of | #1333×D73, #1334×D73, #32995752, … |
| maximal quotient of | #1277×D73, #32977164, #334×Dic73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 3249);