Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #387×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator | C22×C73 | C23×C4 |
| Fitting | #387×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | #387 | D73 |
| hypocenter | C73 | C4×#126 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #387 | |
516 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=ef,c^2=e,d^2=g,b^a=be,c^a=cf,h^c=h^72,h^d=h^721064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#126×D73, C2×#22612481, C4×#17989114, … |
| maximal normal subgroup of | C4×#126×D73, C2×#22612481, C4×#17989114, … |
| maximal quotient of | #33007137, #33007139, #33007158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7060);