Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#17988306 |
| derived, Sylow | C73 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D73 |
| commutator, hypocenter | C73 | C2×C64 |
| Frattini | C32 | C2×D73 |
| Fitting | C2×C32×C73 | C2 |
| socle | C22×C73 | C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
2432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×Dic73, C4×#17988306, #32973788, … |
| maximal normal subgroup of | C64×Dic73, C4×#17988306, #32973788, … |
| maximal quotient of | C4×#17988306, C22⋊#17988306, C4⋊#17988306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 2719);