Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #1306 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556498 |
| commutator | C23×C73 | C42 |
| Frattini | C23×C4 | C2×D73 |
| Fitting | #407×C73 | C2 |
| socle | C22×C73 | #95 |
| hypercenter | #407 | D73 |
| hypocenter | C73 | #1306 |
| LCS | G ▷ C23×C73 ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^72,c^b=cg,d^b=df1034 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1306×D73, C2×#22607840, #32976347, … |
| maximal normal subgroup of | #1306×D73, C2×#22607840, #32976347, … |
| maximal quotient of | #32972554, #32972557, #32972558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 2419);