Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C73 ⋊ #2399 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator, socle | C23×C73 | C24 |
| Frattini | C23 | C23×D73 |
| Fitting | #376×C73 | C2 |
| hypercenter | #376 | D73 |
| hypocenter | C73 | #2399 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 189 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=e,c^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^72,h^c=h^721484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32981057, #32986836, #32986839, … |
| maximal normal subgroup of | #32981057, #32986836, #32986839, … |
| maximal quotient of | #33007728, #33007736, #33007766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7803);