Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C2×#117×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2500 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C2×#117×C73 | C2 |
| hypercenter | C2×#117 | D73 |
| hypocenter | C73 | #2500 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 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=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^721478 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32983636, #32983638, #32995543, … |
| maximal normal subgroup of | #32983636, #32983638, #32995543, … |
| maximal quotient of | #33007956, #33008520, #33009158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 8968);