Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×Q8×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator, socle | C23×C73 | C22×C4 |
| Fitting | C22×Q8×C73 | C4 |
| hypercenter | C22×Q8 | #64408 |
| hypocenter | C73 | #1446 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
736 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=f,c^2=f,b^a=bd,c^a=ce,h^a=h^27,c^b=cf,h^g=h^72404 conjugacy classes — view the full character table.
| maximal subgroup of | #34000694, #34004512, #34004513, … |
| maximal normal subgroup of | #34000694, #34004512, #34004513, … |
| maximal quotient of | #34001294, #34009613, #34009614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19700);