Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11924003 |
| derived, Sylow | C73 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D73 |
| commutator, hypocenter | C73 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D73 |
| Fitting | C2×C4×C8×C73 | C2 |
| socle | C23×C73 | C2×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C4×C8 | |
216 conjugacy classes of subgroups.
2432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32972811, #32972812, #32972823, … |
| maximal normal subgroup of | #32972811, #32972812, #32972823, … |
| maximal quotient of | C2×C8×#11924003, C2×#22607849, M16×#11924003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6097);