Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#14556636 |
| Fitting | C2×C4×D4×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D73 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C22 | C24×D73 |
| Fitting | C2×C4×D4×C73 | C2 |
| socle | C22×C73 | C25 |
| hypercenter | C2×C4×D4 | D73 |
| hypocenter | C73 | C4×H(5,𝔽2) |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
1660 conjugacy classes of subgroups.
1508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32977375, #32977376, #32977382, … |
| maximal normal subgroup of | #32977375, #32977376, #32977382, … |
| maximal quotient of | C4×#17989060, C4×#17989059, C4×#17989062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17715);