Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×M16×C73 ⋊ C4 |
| Sylow | C73 ⋊ #2873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#64408 |
| commutator, socle | C2×C73 | C22×C42 |
| Fitting | C2×M16×C73 | C4 |
| hypercenter | C2×M16 | #64408 |
| hypocenter | C73 | #2873 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
564 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^b=h^27,h^f=h^72428 conjugacy classes — view the full character table.
| maximal subgroup of | #34008623, #34008625, #34008626, … |
| maximal normal subgroup of | #34008623, #34008625, #34008626, … |
| maximal quotient of | #34015647, #34015648, #34015649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21073);