Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #1375 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×#10596842 |
| commutator | C4×C73 | C4×C8 |
| Frattini | C2×C4 | C2×#10596842 |
| Fitting | C2×C8×C73 | C8 |
| socle | C2×C73 | #336 |
| hypercenter | C2×C8 | #10596842 |
| hypocenter | C73 | #1375 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×C8 | |
140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^10,d^b=dg,h^b=h^46,h^d=h^27,h^e=h^72,h^f=h^72188 conjugacy classes — view the full character table.
| maximal subgroup of | #34032815, #34032816, #34032837, … |
| maximal normal subgroup of | #34032815, #34032816, #34032837, … |
| maximal quotient of | #34032858, #34032870, #34032875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21583);