Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #1750 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D73 |
| commutator | C22×C73 | C2×C42 |
| Fitting | C2×C22⋊C8×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D73 |
| hypocenter | C73 | #1750 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=cg,h^a=h^72,h^c=h^721496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1750×D73, C2×#22609699, C4×#17988552, … |
| maximal normal subgroup of | #1750×D73, C2×#22609699, C4×#17988552, … |
| maximal quotient of | #32976475, #32976477, #32976482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4278);