Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×#64408 |
| unambiguous semidirect product | D73⋊(C24×C4) |
| Fitting, socle | C25×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #64408 |
| commutator, hypocenter | C73 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C73 | C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C25 | |
10552 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22625104, #379×#64408, #34015604, … |
| maximal normal subgroup of | C2×#22625104, #379×#64408, #34015604, … |
| maximal quotient of | C24×C4×#64408, C24×C22⋊#64408, C24×C4⋊#64408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21507);