Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #2802 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | #398×C73 | C2 |
| hypercenter | #398 | D73 |
| hypocenter | C73 | #2802 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #398 | |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=efg,b^2=e,c^2=g,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^72,c^b=cg,d^b=de,h^b=h^72,h^c=h^72824 conjugacy classes — view the full character table.
| maximal subgroup of | #33293658, #33293660, #33293676, … |
| maximal normal subgroup of | #33293658, #33293660, #33293676, … |
| maximal quotient of | #33014346, #33014392, #33014582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 12434);