Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic292 |
| Sylow | C73 ⋊ C23×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D292 |
| commutator | C4×C73 | C25 |
| Frattini | C4 | C24×D73 |
| Fitting | C23×C8×C73 | C2 |
| socle | C24×C73 | D4 |
| hypercenter | C23×C8 | D73 |
| hypocenter | C73 | C23×Q16 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1464 conjugacy classes of subgroups.
2360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32992794, #32992796, #32992820, … |
| maximal normal subgroup of | #32992794, #32992796, #32992820, … |
| maximal quotient of | C23×#14556516, C23×#14556525, C22×C4×Dic292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19233);