Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #1452 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C2×C42 |
| Fitting | C4×C8×C73 | C4 |
| hypercenter | C4×C8 | #64408 |
| hypocenter | C73 | #1452 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 | |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^b=cf,h^b=h^27,h^c=h^72,h^e=h^72632 conjugacy classes — view the full character table.
| maximal subgroup of | #34000177, #34000180, #34003366, … |
| maximal normal subgroup of | #34000177, #34000180, #34003366, … |
| maximal quotient of | #34001940, #34001962, #34003351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19724);