Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#17988344 |
| Sylow | C73 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic73 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | C22×M16×C73 | C2 |
| socle | C22×C73 | #95 |
| hypercenter | C22×M16 | D73 |
| hypocenter | C73 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
404 conjugacy classes of subgroups.
1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32973115, #32973117, #32973121, … |
| maximal normal subgroup of | #32973115, #32973117, #32973121, … |
| maximal quotient of | C2×#22607759, #32975382, #32975385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4211);