Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#135×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D73 |
| commutator | C4×C73 | C25 |
| Frattini | C4 | C24×D73 |
| Fitting | C2×#135×C73 | C2 |
| socle | C2×C73 | C23×D4 |
| hypercenter | C2×#135 | D73 |
| hypocenter | C73 | #3584 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×#135 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^d=h^721052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33001688, #33001690, #33001693, … |
| maximal normal subgroup of | #33001688, #33001690, #33001693, … |
| maximal quotient of | #33949545, #33949659, #33950098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19279);