Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #2381 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator | C22×C73 | C23×C4 |
| Fitting | C2×C4⋊Q8×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C2×C4⋊Q8 | D73 |
| hypocenter | C73 | #2381 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^72,c^b=cef,d^b=de1046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32983524, #32983527, #32983529, … |
| maximal normal subgroup of | #32983524, #32983527, #32983529, … |
| maximal quotient of | #33007611, #33007634, #33007638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7691);