Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C73 ⋊ #2862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C43×C73 | C2 |
| hypercenter | C43 | D73 |
| hypocenter | C73 | #2862 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C43 | |
504 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^722348 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32974352, #32974354, #32974444, … |
| maximal normal subgroup of | #32974352, #32974354, #32974444, … |
| maximal quotient of | #33017176, #33017285, #33017321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 12888);