Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #405×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D73 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #405×C73 | C2 |
| socle | C22×C73 | C23×C4 |
| hypercenter | #405 | D73 |
| hypocenter | C73 | C4×#131 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ #405 | |
572 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=e,b^2=f,e^2=g,h^b=h^72,d^c=dg,h^d=h^721520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33001031, #33001036, #33001920, … |
| maximal normal subgroup of | #33001031, #33001036, #33001920, … |
| maximal quotient of | #33051571, C8×#14556599, #33051595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 12932);