Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #340×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2067 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D73 |
| commutator | C22×C4×C73 | C23 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | #340×C73 | C2 |
| socle | C23×C73 | C2×D4 |
| hypercenter | #340 | D73 |
| hypocenter | C73 | #2067 |
| LCS | G ▷ C22×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=de,b^2=dg,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^72,c^b=cf,h^b=h^72,d^c=dg,e^c=eg,f^c=fg,h^c=h^721040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2067×D73, C2×#22611320, #33114596, … |
| maximal normal subgroup of | #2067×D73, C2×#22611320, #33114596, … |
| maximal quotient of | #32990502, #32990509, #32990530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 5899);