Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #117×C73 ⋊ C4 |
| Sylow | C73 ⋊ #2347 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | #117×C73 | C4 |
| hypercenter | #117 | #64408 |
| hypocenter | C73 | #2347 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #117 | |
504 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^27,d^b=de,h^g=h^72410 conjugacy classes — view the full character table.
| maximal subgroup of | #34006906, #34006907, #34006914, … |
| maximal normal subgroup of | #34006906, #34006907, #34006914, … |
| maximal quotient of | #34014684, #34014697, #34014705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21021);