Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ Q8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator | C22×C73 | C23×C4 |
| Fitting | #384×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | #384 | D73 |
| hypocenter | C73 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #384 | |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^d=h^721058 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32980155, #32980159, #32980183, … |
| maximal normal subgroup of | #32980155, #32980159, #32980183, … |
| maximal quotient of | #33007420, #33007424, #33007468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7422);