Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic146 |
| Sylow | C73 ⋊ Q8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D73 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | C4×M16×C73 | C2 |
| hypercenter | C4×M16 | D73 |
| hypocenter | C73 | Q8×M16 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
388 conjugacy classes of subgroups.
1490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32980318, #32980322, #32980332, … |
| maximal normal subgroup of | #32980318, #32980322, #32980332, … |
| maximal quotient of | M16×C4⋊Dic73, M16×#11924007, #33084633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13463);