Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #135×C73 ⋊ C4 |
| Sylow | C73 ⋊ #2943 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×#64408 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C4 | C23×#64408 |
| Fitting | #135×C73 | C4 |
| socle | C2×C73 | C2×C4×D4 |
| hypercenter | #135 | #64408 |
| hypocenter | C73 | #2943 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^46,e^b=eg,h^c=h^27,h^f=h^72296 conjugacy classes — view the full character table.
| maximal subgroup of | #34012604, #34012605, #34012606, … |
| maximal normal subgroup of | #34012604, #34012605, #34012606, … |
| maximal quotient of | #34018268, #34018269, #34018270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21264);