Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C2×D73 |
| commutator, socle | C2×C73 | C22×C16 |
| Frattini | C16 | C22×D73 |
| Fitting | C2×C32×C73 | C2 |
| hypercenter | C2×C32 | D73 |
| hypocenter | C73 | #2258 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C32 ◁ C2×C32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^722384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32973796, #32973798, #33006546, … |
| maximal normal subgroup of | #32973796, #32973798, #33006546, … |
| maximal quotient of | #33006162, #33006163, #33006179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6803);