Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C23×#11924012 |
| Sylow | C73 ⋊ C23×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D73 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C4 | C24×D73 |
| Fitting | C24×C4×C73 | C2 |
| socle | C24×C73 | C2×C4 |
| hypercenter | C24×C4 | D73 |
| hypocenter | C73 | C23×M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4 | |
1720 conjugacy classes of subgroups.
2384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32991211, #32991213, #32991219, … |
| maximal normal subgroup of | #32991211, #32991213, #32991219, … |
| maximal quotient of | C23×#14556502, C22×C4×#11924012, C23×C22⋊#10596831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19212);