Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | D4×#11924036 |
| Sylow | C73 ⋊ C2×C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C22 | C23×#64408 |
| Fitting | C4×D4×C73 | C4 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C4×D4 | #64408 |
| hypocenter | C73 | C2×C8×D4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
616 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #34003641, #34003649, #34003657, … |
| maximal normal subgroup of | #34003641, #34003649, #34003657, … |
| maximal quotient of | D8×#11924036, SD16×#11924036, Q16×#11924036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21213);