Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#10596831 |
| Sylow | C73 ⋊ C2×C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D73 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | C2×C4×D4×C73 | C2 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C4×D4 | D73 |
| hypocenter | C73 | C2×C8×D4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
616 conjugacy classes of subgroups.
1520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×#10596831, #32976528, #32976532, … |
| maximal normal subgroup of | #99×#10596831, #32976528, #32976532, … |
| maximal quotient of | C2×D8×#10596831, C2×SD16×#10596831, C2×Q16×#10596831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13183);